Steven Caulker put the hosts ahead in first-half stoppage time at the Cardiff City Stadium on Saturday, and although Lewis Holtby levelled matters in the second half, Caulker netted again before a Sascha Reither own goal secured the points for Ole Gunnar Solskjaer's side.
The Cottagers remain four points adrift of safety, as 17th-placed Albion were beaten 3-0 by Manchester United in a result that places further doubt on the future of Pepe Mel less than two months after his Hawthorns appointment.
Sunderland are likely to have been encouraged by the day's results despite dropping to second from bottom. The Black Cats, in FA Cup quarter-final action on Sunday, have two or three games in hand on the teams around them.
Palace were unable to put any more distance between themselves and the bottom three after a first-half defensive mix-up allowed Jay Rodriguez to give visitors Southampton a 1-0 victory.
The Eagles are two points behind Norwich, who were held to a 1-1 draw by Stoke at Carrow Road. Jon Walters followed up his match-winning penalty against Arsenal last weekend with another spot-kick to cancel out Bradley Johnson's header. The Republic of Ireland striker was then sent off, but Stoke survived to take a point.
The day began with Manchester United's trip to the Black Country, where Mel's winless start to his West Brom reign was stretched to eight games.
Phil Jones overcame a hip injury in time to start for David Moyes' men, and it was the centre-back who opened the scoring with a glancing header in the 34th minute from a free-kick by Robin van Persie.
Van Persie was fortunate not to collect a second booking from referee Jonathan Moss when he slid in on Steven Reid, and Moyes chose to substitute the Dutchman within 10 minutes.
Wayne Rooney then doubled United's lead with a close-range header from Rafael's cross, and van Persie's replacement Danny Welbeck sealed the three points on 82 minutes when he lifted the ball over Ben Foster following Rooney's pass - his 10th Red Devils goal of the season. United move into the top six on goal difference from Everton, who have a game in hand.
At Cardiff, Fulham boss Felix Magath surprisingly started with record-signing Kostas Mitroglou - despite the Greek striker's recent fitness issues - and teenage striker Cauley Woodrow, who was playing on loan at League Two Southend earlier in the season.
But the hosts had the better of the first half and deservedly took the lead shortly before the interval when a deflected Craig Noone shot fell to captain Caulker for an easy tap-in.
That ended a league goal drought of over seven hours for Cardiff, but they were pegged back on 59 minutes. Giorgos Karagounis whipped a corner into the box, where the ball glanced off the head of John Heitinga before Holtby side-footed home.
However, just eight minutes elapsed before Cardiff regained the advantage. Jordon Mutch's ball in was headed down by Caulker and the ball bounced over goalkeeper Maarten Stekelenburg, who really should have done better.
Four minutes later, the Bluebirds secured a vital victory when Mutch managed to get his head to Noone's cross and Stekelenburg made a good close-range stop, only to see the loose ball deflect off Riether's head and into the goal. It was only Solskjaer's second league win in nine games since taking over in January.
Meanwhile, in south-east London, Jason Puncheon was back in the Crystal Palace team to face Southampton as one of three changes made by Tony Pulis.
A defensive error in the 37th minute settled the encounter. Kagisho Dikcagoi's header back on the halfway line was seized upon by Rodriguez, who raced towards the Palace goal. Julian Speroni came out of his box to slide in but the ball fell favourably to the grounded Rodriguez, who poked the ball home from outside the area.
After Daniel Sturridge (18), Rodriguez is level with Rooney on 11 goals as the highest-scoring Englishmen in the Premier League this season.
Palace enjoyed a series of set pieces late on in the second half but ninth-placed Saints held on to return to winning ways.
Despite not having scored since the opening day of the season, Norwich striker Ricky van Wolfswinkel was recalled to face Stoke by Chris Hughton after the 4-1 humbling at Aston Villa last Sunday. Peter Odemwingie came in for the suspended Charlie Adam for the visitors.
On 56 minutes, a Robert Snodgrass free-kick from wide right was headed home by Johnson, rising above Ryan Shawcross.
But Mark Hughes threw on on-loan John Guidetti for Odemwingie soon afterwards and saw the young Sweden striker claim a 73rd-minute penalty when Sebastien Bassong brought him down in the box.
Walters did the honours from the spot - but the Stoke scorer was sent off shortly afterwards for a high, late challenge on Alexander Tettey. Despite the red card, Stoke hung on for a draw.
In the evening kick-off at Stamford Bridge, Chelsea beat London rivals Tottenham 4-0 to extend their lead at the top of the table to seven points over Liverpool and Arsenal.
After a goalless first half, Samuel Eto'o - a late inclusion after Fernando Torres withdrew following the warm-up - broke the deadlock on 56 minutes after being gifted the ball by a hapless Jan Vertonghen before he was fouled by Younes Kaboul for a spot-kick four minutes later which appeared soft.
The France defender was shown a straight red card for denying a clear goalscoring opportunity and Eden Hazard sent Hugo Lloris the wrong way with Chelsea's second goal in five minutes before Ba's late double added to Spurs' humiliation.
The victory extended Mourinho's unbeaten Premier League home record to 75 games.