A resurgent Cardiff pulled away with two second-half goals in a thrilling contest in South Wales to join their opponents on five points from nine matches.
The Bluebirds had gone eight top-flight matches without a win this term heading into Saturday afternoon's clash, including five defeats on the spin, but this much-needed victory takes them up to 17th place in the standings.
Fulham took the lead against the run of play at the Cardiff City Stadium through a 30-yard strike from Andre Schurrle, which flew into the top-right corner of the goal.
The Cottagers had the worst defensive record in the division prior to this weekend's matches, though, and Cardiff were soon able to take advantage of their opponents' poor defensive setup.
Joe Bennett then shot wide from the edge of the area, but the Welsh side did not have to wait too much longer for a second as Bobby Reid kept his cool to slip his shot under Bettinelli after Schurrle got caught in possession.
Etheridge did better the next time Sessegnon was played through, racing off his line to thwart the first teenager to score in the Premier League this season, while Murphy and Harry Arter both sent shots over the bar up the other end.
Just when momentum looked to be swinging the visitors' way, with Sessegnon's latest effort - a long-range curler - being tipped over the bar by Etheridge, the Bluebirds edged in front and did not look back.
Fulham could have left the Welsh capital with a share of the spoils as former Swansea City defender Alfie Mawson's header was destined for the back of the net, if not for the intervention of Etheridge.
CARDIFF CITY (4-3-3): Etheridge; Ecuele Manga, Morrison, Bamba, Bennett; Gunnarsson (Richards 77'), Arter (Damour 86'), Camarasa; Reid, Murphy (Harris 82'), Paterson
FULHAM (4-3-3): Bettinelli; Chambers (Mawson 46'), Ream, Odoi, Le Marchand; Johansen (Vietto 82'), McDonald, Seri (Ayite 58'); Schurrle, Mitrovic, Sessegnon