Somehow, a thrilling first-half ended goalless, but Dominic Solanke opened the scoring just moments into the second with a deft finish. From then on it was all Fulham, as the hosts created chance after chance to no avail until Tosin glanced home a brilliant cross from skipper Tom Cairney.
The result sees Fulham stay top of the Championship table, while Bournemouth remain breathing down their necks in 2nd.
Story of the game
There was just the one change to the Fulham side that drew with Preston North End last time out, with Joe Bryan replacing Antonee Robinson — dropped from the squad due to illness — at left-back, while club captain Cairney made a welcome return to the matchday squad on the bench.
On his return to Craven Cottage, Bournemouth manager Scott Parker made three adjustments following the dramatic draw at home to Coventry City last weekend, one of them enforced as the suspended Jefferson Lerma missed out. Chris Mepham and Gavin Kilkenny were also dropped to the bench with Gary Cahill, Adam Smith and Emiliano Marcondes coming into the starting line-up.
It was a simply electric atmosphere at Craven Cottage for the clash of two Championship heavyweights, and the match started at a suitably frenetic pace.
The first chance of the match fell to the visitors when Ryan Christie made a surging run down the right and passed across for Adam Smith on the edge of the box. The full-back did brilliantly to evade Denis Odoi and shift the ball onto his stronger right foot in one swift motion, but his resultant effort was saved comfortably by Marek Rodak.
Fulham went straight down the other end and worked an opportunity of their own to score an early goal. Neeskens Kebano received the ball on the left and meandered his way into the area, eventually drawing a fine save from Mark Travers at his near post.
So, both goalkeepers had been given early chances to warm their palms on a chilly evening at the Cottage, and they'd surely be presented with plenty more as the game progressed.
Kebano was proving too hot to handle for Jack Stacey on the right of Bournemouth's defence. With 10 minutes on the clock he received the ball on the left edge of the box and taunted Stacey into the tackle before shimmying past him and striking at goal, but again Travers did well to tip the ball wide.
Fulham had another chance from the following corner when Tosin headed back across goal for Fabio Carvalho just a handful of yards out, but Gary Cahill did brilliantly to sniff the danger and clear his lines before the forward could shoot.
Lewis Cook was playing with fire when he put in a high tackle on Kebano and was perhaps fortunate to escape with just a booking, but such was Bournemouth's frustration at their inability to contain the Congolese forward thus far.
Having been on the back foot for 15 minutes or so, Bournemouth mustered two good chances to take the lead in quick succession. First, Jaidon Anthony fed Stacey's overlap and the wing-back crossed for Solanke who couldn't direct his glancing header on target. Emiliano Marcondes then recycled possession and whipped another ball in for Solanke, whose next headed effort flew just wide of the post.
At the other end of the pitch, Joe Bryan then crossed right onto the head of top scorer Aleksandar Mitrovic — Fulham's arch marksman rarely passes up chances like that, but it nicked off his shoulder and behind for a goal-kick.
Leading the line for the visitors, Solanke was, as expected, proving a real handful. With 30 minutes gone he received the ball from Lewis Cook on the left and cut his way infield before scooping his way past Tosin and fizzing a vicious effort across goal which missed the target by the finest of margins.
The next chance for Mitrovic came when a good run in behind by Harrison Reed was fed by Bryan. Reed then crossed into the centre for Mitrovic but it was at an awkward height for the striker and he failed to get proper contact on the ball.
Moments later, Carvalho won the ball high up the pitch and exchanged a neat one-two with Mitrovic before whipping a ball into the middle where Kebano had made a run, but Stacey made a crucial intervention to nick the ball behind for a corner.
Fulham were demanding a penalty on the 40-minute mark after a coming together between former Cherry Harry Wilson and Solanke in the box, but referee Tim Robinson deemed there was nothing doing.
The two best chances of the match fell on the cusp of half-time. Kebano picked up a loose ball in midfield and played in Mitrovic behind the Bournemouth defence. The Serb had all the time in the world to think about his finish but took one touch too many and saw his eventual shot blocked superbly on the line by Steve Cook. Carvalho was granted a second bit at the cherry, but the Bournemouth skipper bailed his team out once again.
Cook's heroic defending earned him a series of embraces from his teammates and rapturous applause from the travelling support, and it was that which ensured the match would remain deadlocked at the interval.
Remarkably, within ten seconds of the restart, Bournemouth were ahead. It was a lofted pass from Philip Billing straight from kick-off and Odoi failed to track the run of Solanke. The striker's touch was immaculate and he had the finish to match, scoring his 16th goal of the season to put his side ahead in this, the biggest match of the Championship season thus far.
As if this game wasn't action-packed enough already.
Straight down the other end, Kebano latched onto a poor attempted clearance by Stacey, chested it down and struck at goal on the half-volley, but Travers was equal to it. The remaining 45 minutes were likely to be the longest of Bournemouth have experienced in a long while.
Wilson nearly levelled the scoring in spectacular fashion when he cut inside from the right and fired a vicious effort towards the far top corner, but it whistled just wide of the target.
It was all Fulham now, as Parker threw on Ben Pearson for Marcondes in a bid to shore-up his midfield. On the hour mark, a sumptuous set-piece delivery from Jean-Michael Seri landed right on the head of Mitrovic. The striker's effort looked destined to nestle in the top corner but, somehow, the ball flew behind with Travers stranded on the spot.
This game was getting scrappier by the minute snd there was only one team that suited — Fulham were finding their possession-based football increasingly disrupted and Bournemouth licked their lips at the sight of defensive gaps left behind when the hosts surged forward.
Fulham's best chances of equalising were always going to be through their top scorer, but he lacked his usual clinical edge this evening. With just under 15 minutes remaining, Cairney received a short corner from Wilson and crossed for the striker, who did brilliantly to hold off Smith and Pearson simultaneously before making contact on the ball, but Travers was equal to it.
The introduction of Cairney had at least added another dynamic to Fulham's approach play. Just moments later he fed a clever reverse-pass in behind the Bournemouth defence for Kebano, but the forward's touched just closed the angle too much and Travers was always going to save at his near post.
Travers was proving absolutely impervious in goal for the visitors. Mitrovic was again sought out by an inch-perfect delivery by Wilson from a free-kick and his header across goal looked destined for the net, but the goalkeeper stretched every fibre of his being to beat the ball away.
Fulham had been knocking on the door and then some and, with 83 minutes on the clock, they got their just rewards. Cairney's impact since being brought on was undeniable and he summoned up the good once again with a superb in-swinging cross which was glanced home by Tosin.
They had deserved that, and now the hosts started pushing for the winner — but amidst the onslaught Bournemouth held strong and denied the hosts any goalscoring opportunities at all after their equaliser, meaning the points were shared in the Championship's game of the season so far.
Fulham: Rodak; Odoi, Tosin, Ream, Robinson; Seri (Cairney 70'), Reed; Wilson, Carvalho (Decordova-Reid 70'), Kebano; Mitrovic.
Unused subs: Gazzaniga, Tete, Hector, Onomah, Muniz.
AFC Bournemouth: Travers; Stacey, S Cook, Cahill, Smith (Mepham 88'); L Cook, Marcondes (Pearson 56'), Billing; Christie, Solanke, Anthony (Brady 88').
Unused subs: Nyland, Gilkenny, Rogers, Lowe.
Referee: Tim Robinson
Following this draw here, Fulham travel to Bedfordshire to face Luton Town on Saturday.