After a cautious opening period, the game burst into life in the second half, as Neil Warnock's men looked to earn vital points in their battle to stave off relegation.
Cottagers' 'keeper Sergio Rico denied the visitors on numerous occasions in the final half-hour, with Junior Hoilett hitting the bar late on, as the hosts held on to likely condemn Cardiff back to another season in the second tier - along with Fulham.
Stakes high for visitors
With the stakes high for the visitors and the with the chance to close the gap on Brighton & Hove Albion in 17th spot, the Seagulls began cautiously, all-too aware of their precarious top flight position.
The hosts although already condemned to a immediate return to the Championship next season but coming into the game with good form, also began thoughtfully.
As if to pave the way for a disappointing opening period, it took 12 minutes for the games first effort, as Aleksandar Mitrovic shied from the edge of the box, only for the Serbian's strike to be palmed away by Bluebirds' stopper Neil Etheridge.
Both sides were equally culpable of conceding possession in the midfield, in particularly Fulham, who were seeking width on the left channel for the ever-eager Babel to scamper forward down the Cardiff right.
The first half was largely marked by a nasty incident involving Cottagers defender Denis Odoi. As the right-back chased back for a ball with Nathaneel Mendez-Laing, Odoi stopped to clear an errant ball, but was caught with a kick to the head by teammate Maxime Le Marchand. A nine-minute stoppage ensued, as Odoi was stretchered off.
As the game resumed, neither set of players could get going with any meaningful verve, before it was the energetic Babel who looked to grab the lead before the break.
The Dutchman was denied from close range in stoppage time, before he turned provider for Mitrovic, but the forward could only slice wide from an attempt on the half-volley. The half-time whistle blew with the score goalless.
After an opening period of little chances, both sides began on resumption with greater intensity. Indeed it was Mitrovic who spurned the games clearest opening thus far.
After Ryan Sessegnon had cut his way down the right, the England international slid a slide-rule pass across the Cardiff box for the waiting number nine. Mitrovic could only sky his shot however, blazing over the bar.
Cairney was finding the ball on a more regular basis for the hosts in central areas, but it we he whose cross-cum shot from wide left, that had to be tipped over the bar by Etheridge for a corner.
Cardiff however were having their own openings, and after Mendez-Laing cleverly worked an opening by dispossessing Joe Bryan on the bye-line, cut back a low cross for the waiting Leandro Bacuna, only for his pass to be diverted away from danger by Ream.
At the other end, Mitrovic was continuing to have another of his errant days, with the Fulham marksman again shooting high and wide of Etheridge's goal from 25 yards.
Babel rocket stuns Bluebirds
With less than 15 minutes to go on the Thames, the game seemed to be heading for a stalemate. Babel however had other ideas. The Dutchman had always seemed the most likely to be involved in a winner and duly obliged.
Finding space on the right-hand edge of the box from Cyrus Christie's ball, Babel aimed his sights on goal and unleashed a curling effort dipping past Etheridge and into the top-right corner of the net as Craven Cottage erupted.
With the visitors set for a potentially terminal blow, Warnock's men responded in desperation.
Cardiff flew forward and were denied on multiple occasions as the 90-minute mark approached. Substitute Rhys Healey saw his header saved by the increasingly industrious Rico, before Junior Hoilett saw his effort clatter off the bar, after Bobby Reid fed the Canadian international having been put through on goal.
Rico was again forced into action as the Bluebirds piled forward to grab what could yet have been a vital point saving from a multitude of set-pieces that fell to the lively Healey, but the Whites 'keeper was bent on keeping the opposition out in a frantic finish.
As time ran out on a polar opposite second period to that of the first half, Cardiff's players sank to their knees, now reliant on a favour from Newcastle in the late kick off.