Babel scored his third goal in four matches with a scorching curler from 25 yards to secure a 1-0 victory and leave City’s plight looking increasingly bleak.
Fulham’s run of decent form under caretaker boss Scott Parker has come too late to save them, and Babel’s thunderbolt may well have helped drag Cardiff back down with them.
The match was overshadowed by what appeared a horrific injury to Denis Odoi, who stooped to head the ball clear and took a boot in the face from his Fulham team-mate Maxime Le Marchand.
The defender appeared to have been out cold as he crumpled to the floor, and although he initially got back to his feet he then required treatment for eight minutes before eventually being taken off on a stretcher wearing an oxygen mask.
Thankfully Odoi was later said to be fine and did not need to be taken to hospital.
Predictably Cardiff were not lacking in effort or spirit, but they carried little goal threat until Junior Hoilett struck the cross bar late on.
Hoilett threatened occasionally down the right but his shot, into the side-netting, was the closest the visitors came to disturbing Fulham goalkeeper Sergio Rico in the first half.
During nine minutes of added time at the end of the half, Babel got free down the left and pulled the ball back but Ryan Sessegnon’s weak volley bounced wide.
Moments into the second half Aleksandar Mitrovic should have given Fulham the lead.
Tom Cairney raided down the right and squared across goal but Mitrovic, who ended a nine-match run without a goal in the win at Bournemouth last weekend, blazed over.
The Serbian then turned Sean Morrison on the edge of the area but once again lifted his shot over the crossbar.
Cardiff’s chances were few and far between with Victor Camarasa, their liveliest player, off target with an ambitious effort from 30 yards and Nathaniel Mendez-Laing firing straight at Rico.
And with 11 minutes remaining Babel collected the ball from Cyrus Christie and hit a fierce first-time shot which curled away from Etheridge as it flew into the top corner.
There was late agony for Cardiff when Rico tipped Danny Ward’s header over before Hoilett’s curler rattled the crossbar.