West Brom blew a three-goal lead in a six-goal thriller at home to Tottenham, while Crystal Palace climbed up to 12th in the table after edging Aston Villa.
Newcastle United, meanwhile, continue to see their season peter out to a tame conclusion after suffering defeat at in-form Stoke City.
Hugo Rodallega scored the winner for the second week in a row as Fulham closed the gap on Norwich City to two points following a nerve-jangling 1-0 win at Craven Cottage.
Fulham grabbed the only goal five minutes before half-time when Steve Sidwell flicked on Lewis Holtby's free-kick from the left and Rodallega swept the ball home from close range.
Norwich, under Neil Adams for the first time following the sacking of Chris Hughton, now face a daunting final four games against Liverpool, Manchester United, Chelsea and Arsenal in their fight for survival.
Juan Cala fired home an unlikely winner as Cardiff picked up a surprise 1-0 victory at Southampton to sit just three points from safety.
Cardiff made the breakthrough 20 minutes into the second half when Cala, who had remained forward following a set-piece, steadied himself on the edge of the box before drilling a left-footed shot beyond Paulo Gazzaniga.
Everton climbed above Arsenal in the quest for UEFA Champions League football after Wes Brown's own goal condemned Sunderland to a 1-0 defeat at the Stadium of Light.
The hosts fell behind in luckless circumstances with 15 minutes to go when Gerard Deulofeu got down the right and the on-loan winger's cross was turned into his own net by Brown, whose side are seven points from safety with six games to play.
Crystal Palace beat Aston Villa 1-0 at Selhurst Park to leapfrog their opponents in the table and continue their excellent form under Tony Pulis.
Palace edged ahead in the 76th minute when Yannick Bolasie's cross fell to Jason Puncheon and he turned Ryan Bertrand before firing a low shot in off the post.
West Brom fluffed a golden chance to edge closer to survival after Tottenham came from three goals down to snatch a 3-3 draw at The Hawthorns.
The home side were in front after just 28 seconds when Morgan Amalfitano's low cross from the right was pushed out by Hugo Lloris straight to Matej Vydra, who fired home.
The lead was doubled just three minutes later following another cross from the right as Steven Reid's centre was helped on to the far post where Chris Brunt was waiting to volley past Lloris.
Spurs wasted the chance to pull a goal back on 16 minutes when Emmanuel Adebayor's weak penalty was easily saved by Ben Foster after Amalfitano had nudged Danny Rose over.
Pepe Mel's side notched a third goal just past the half-hour mark when Younes Kaboul's misguided header allowed Stephane Sessegnon a run on goal and, after he had held off Vlad Chiriches, he finished beyond Lloris.
The visitors did get a goal back on 34 minutes thanks to a slice of good fortune as Kyle Naughton's low cross deflected off Jonas Olsson and looped over goalkeeper Foster.
Spurs scored again with 20 minutes to go when Aaron Lennon found space on the right and his chipped cross to the six-yard box was headed home by Harry Kane.
And, in the fourth minute of added time, Spurs pinched a point when the ball found its way to Christian Eriksen in the box and he smashed a fine shot into the top corner.
Stoke cemented their position in the top half of the table after Erik Pieters' fluky first-half goal secured a 1-0 win over Newcastle at the Britannia Stadium.
In a largely uneventful encounter, Stoke scored the only goal three minutes before half-time when Pieters' attempted cross from the left flew over Tim Krul and bounced in off the post.