Substitute Shane Long struck twice late on as second-placed Southampton stayed within touching distance of the leaders with a 2-0 win over Leicester at St Mary's Stadium.
Both sides struggled in awful conditions on the south coast with Sadio Mane closest to a first half opener when his close-range effort was ruled out for offside.
Former Newcastle goalkeeper Fraser Forster was once again in top form, as he looks to a place in the Champions League, following his European trips with Celtic.
Diego Costa fired his 10th goal of the season as Chelsea maintained their four-point lead at the top of the Barclays Premier League with a 2-1 win over Liverpool at Anfield.
Costa polished off a Cesar Azpilicueta cross in the 67th minute as Jose Mourinho's men fought back from the shock of conceding an eighth minute opener to Emre Can.
The Turkish midfielder's effort deflected home off Chelsea defender Gary Cahill, who redeemed himself five minutes later when he bundled an equaliser past home keeper Simon Mignolet.
Costa's effort appeared to have sealed victory but Chelsea still had to ride their luck when an apparent Cahill handball in the box went unpunished by referee Anthony Taylor.
Sergio Aguero saved Manchester City further embarrassment with a double in a 2-2 Premier League draw at QPR in the late game at Loftus Road.
Manuel Pellegrini admitted the champions were in the midst of a crisis of confidence following their latest European defeat and QPR seemed determined to increase City's misery at Loftus Road.
Charlie Austin scored the opening goal after finding the City net for the third time after 21 minutes.
Austin had two strikes ruled out in the space of 30 seconds after eight minutes, but each time the visitors' shambolic defence was reprieved.
He was offside in heading in, then City goalkeeper Joe Hart kicked the ball twice, firstly with his standing foot, before the striker scored. Referee Mike Dean correctly ruled out the effort.
Hart made a stunning save from Austin after 14 minutes before it was fourth time lucky as the striker ghosted in behind an absent City defence, was played on by Eliaquim Mangala, and finished clinically for his sixth of the season.
Aguero, who was excellent throughout, was given the benefit of the doubt by the officials when he equalised, despite the possibility of the strike being ruled out for offside and handball.
Austin's cross was then turned into his own net by Martin Demichelis but Aguero mesmerised the QPR defence for a second time to earn a draw.
Third-placed City now have one win in six games and are eight points behind leaders Chelsea.
Yannick Bolasie missed a good chance but Manchester United rode their luck against Crystal Palace and grabbed the winner in the 67th minute when substitute Juan Mata played a neat one-two with Angel di Maria before firing home.
Mata also hit the post late on as United improved and ultimately did just enough to earn their victory.
Burnley claimed their first top-flight win at the 11th time of trying as they edged a 1-0 win over Hull at Turf Moor.
Recalled Ashley Barnes was the hero as he headed home Kieran Trippier's 50th minute cross to finally get Sean Dyche's season up and running.
Andy Carroll came agonising close to claiming all three points for West Ham in his first appearance of the season at Upton Park.
The Hammers were largely frustrated by a resolute Aston Villa side who were looking to end a miserable run of six successive defeats.
Diafra Sakho missed two late chances before Carroll replaced Mark Noble in stoppage time and saw a strong late header brilliantly saved by Brad Guzan as Villa clung on for a goalless draw.