Hugo Rodallega hit the winner for Fulham as the Londoners edged their battle with another side in the scrap at the bottom, Norwich, at Craven Cottage.
Rodallega struck five minutes before the break with Norwich having threatened when Robert Snodgrass hit the crossbar from a free-kick.
The result tightened the table just outside the relegation zone, leaving Norwich - who spurned numerous other opportunities in their first game since parting company with manager Chris Hughton - just two points above 18th-placed Fulham.
1 Liverpool 74
2 Chelsea 72
3 Man City 70
4 Everton 66
5 Arsenal 64
6 Tottenham 60
7 Man Utd 57
8 Southampton 48
9 Newcastle 46
10 Stoke City 43
11 West Ham 37
12 C Palace 37
13 Hull City 36
14 A Villa 34
15 Swansea 33
16 West Brom 33
17 Norwich 32
18 Fulham 30
19 Cardiff 29
20 Sunderland 25
Juan Cala was the Cardiff hero, scoring the only goal of the Welsh side's victory at Southampton.
Cardiff were on the back foot for much of the game, not least when a deflected Gaston Ramirez shot crashed back off the crossbar.
But Ole Gunnar Solskjaer's men, who remain 19th, held firm and picked up the three points when Cala struck from just outside the box in the 65th minute.
Those results cut Sunderland four points adrift at the bottom of the table after Gus Poyet's men went down 1-0 at home to Champions League hopefuls Everton.
The Wearsiders had a number of good chances but failed to take advantage and they were caught out after 75 minutes as Gerard Deulofeu's cut-back was diverted into his own net by Wes Brown.
Everton's victory took them above Arsenal, who were in FA Cup action, into fourth.
Christian Eriksen scored an injury-time equaliser as Tottenham completed a remarkable comeback from 3-0 down to draw 3-3 at West Brom.
The Baggies had looked like boosting their survival hopes as they raced into a 2-0 lead at The Hawthorns through goals from Matej Vydra and Chris Brunt inside the first four minutes.
Ben Foster then saved a penalty from Spurs' Emmanuel Adebayor before Stephane Sessegnon added a third for West Brom.
But Tottenham were not finished, pulling one back as Jonas Olsson deflected a Kyle Naughton cross past Foster before the break and Harry Kane then headed home.
Spurs still had 20 minutes to find an equaliser and Eriksen provided it in the fourth minute of injury time to deny West Brom a first home win under Pepe Mel.
Crystal Palace claimed another three crucial points in their survival battle as Jason Puncheon secured a 1-0 win over Aston Villa at Selhurst Park.
Puncheon fired in off the post 14 minutes from time after Cameron Jerome had earlier squandered a fine chance by hitting the bar from close range.
Puncheon hit the woodwork late on as Villa suffered their fourth successive defeat, leaving them with work still to do to secure their top-flight status.