The Blues needed goals from Baines, Oumar Niasse and Dominic Calvert-Lewin to grab the points from the Hornets after Richarlison and Christian Kabasele opened the scoring for the visitors.
Former Everton midfielder Tom Cleverley also fired a 99th-minute penalty wide after Jordan Pickford had fouled Richarlison.
The first-half at Goodison Park failed to explode into life on Bonfire Night, despite there being multiple chances at either end but it was the Hornets, 30 seconds after the half-time break, that opened the scoring.
A long ball cleared by the Watford backline bounced over Jonjoe Kenny and André Carillo knocked it on to Andre Gray. The former Burnley man beat Kenny and chipped a ball across to Richarlison.
With Pickford beaten, the Brazilian poked home from only a couple of yards to give the visitors the lead.
Whoever takes over at Goodison Park has got plenty of problems to rectify, none more so than the porous defence that hasn’t kept a clean sheet since the early part of September.
A corner from Jose Holebas found a waiting Kabasele, stood in front of Phil Jagielka, as the defender headed powerfully into Pickford’s bottom right-hand corner.
The Blues responded quickly as Oumar Niasse bundled home after beating an onrushing Orestis Kamezis. The Greek international, who replaced an injured Heurelho Gomes, charged out of his area to clear a long ball from Ademola Lookman but found himself stranded as Niasse bundled home.
Calvert-Lewin, on for Wayne Rooney following the Everton goal, nodded home from a corner to draw the Blues level with 20 minutes to play.
It was then the turn of Baines, as stoppage time began to put the ball home from the penalty spot. Late substitute Aaron Lennon was fouled by Holebas as referee Graham Scott pointed to the spot.
The reliable left-back slotted home to give the Blues all three points.
Blues better but work to do in attack
Compared to recent games, Everton were much better going forward and gave Marco Silva’s side something to respect despite their dire form.
The majority of the Blues’ good play came from Kenny and Gylfi Sigurdsson on the right-hand side as they looked to attack Holebas.
Yet it was Watford who carved out the first chance. Will Hughes’ pressure forced Kenny to turn the ball behind for a corner. The returning Cleverley took it short and whipped in a dangerous return ball.
His cross nearly caught Pickford out but the effort was only marginally high and wide over the keeper’s far post.
Everton’s energetic duo of Tom Davies, playing behind the striker, and Oumar Niasse kept the Watford backline in check.
Their pressure forced Gomes to send wayward balls into both the Main Stand and Bullens Road on a number of occasions but it took the Blues half an hour to force the Brazilian into action.
Baines forced a save from Gomes after good work from Niasse, Davies and Rooney on the right-hand side. The left-back, unmarked, fired his effort right at the Brazilian after a delightful Rooney cut-back.
With the half coming to a close, Watford had a number of chances to take the lead.
Richarlison broke behind the Everton back line after a superb through ball from Gray. Pickford came rushing out of his area but misjudged it. Baines, doing his best on the last-ditch effort, forced the Brazilian wide and forced the forward to fire wide of the empty net.
From there, it was all the visitors.
The in-form Abdoulaye Doucoure fired a powerful effort from just outside the 18-yard-box directly at Pickford as Watford began turning the screw with five minutes left to play in the first-half.
Summer signing Hughes then had a shout for a penalty after he was bundled over by Idrissa Gana Gueye. Referee Graham Scott waved his shout away and awarded a goal kick.
At the half, the travelling Hornets would be disappointed not to found the back of the net as Scott blew for half-time.
Visitors start quickly after the break
Going into the break unlucky not to be in front, the Hornets stung quickly to take the lead.
Richarlison, labelled as the danger man before the game, sent the visiting fans wild as he wheeled away after prodding home past Pickford moments after the break.
The Blues responded quickly and forced Gomes into a save with 53 minutes played.
Energetic work from Niasse deep into the Watford half against Miguel Britos knocked a ball across to Sigurdsson but his effort was easily saved by Gomes.
Rooney then pounced on the loose ball and tried to work a ball back across the Brazilian keeper’s box but the former Tottenham Hotspur man went down and needed lengthy treatment after pushing away the cross.
Kabasele, who challenged Niasse to the Rooney cross, landed on Gomes and after a lengthy spell of treatment, the keeper had to be replaced by Kamezis.
It was the defender who injured his own goalkeeper who doubled Watford’s lead moments later. The former Genk man headed home from a Holebas corner after getting free of his marker, Phil Jagielka.
The late, late show
Niasse latched on a long-ball by substitute Ademola Lookman and went round an onrushing Kamezis.
Despite being brought down by Kababsele just before knocking home, Niasse and the ball rolled over the goal line to give the Blues a foothold back into the game.
Calvert-Lewin nodded home from a corner after good work from Jonjoe Kenny and Lookman on the far-side. The youngster nodded home past the beaten Greek keeper as he was blocked off by Jagielka.
Back on level terms and with the Goodison faithful behind them the Toffees went in search of a winner and found one.
Late substitute Aaron Lennon was bundled over on the right-hand side of the Watford box and referee Scott subsequently pointed for a penalty.
The ever-reliable Baines powered home to give the Blues a late 3-2 lead and the victory.
The Blues now sit 15th in the Premier League table whilst the visitors move up to eighth.