Watford claimed a potentially crucial three points in the battle for Premier League survival on Saturday, and there were also wins for Leicester, Everton and Brighton - while Norwich drew with Tottenham and Crystal Palace were held by Southampton.
Watford, who look a new team under Nigel Pearson, are now two points behind Aston Villa and only three points from safety thanks to Troy Deeney's double and Ismaila Sarr's clincher against Dean Smith's side.
Deeney opened the scoring from a rebound after Tom Heaton saved Abdoulaye Doucoure's shot. The Hornets had Adrian Mariappa sent off for a second booking, but still managed to score twice more.
Boyhood Birmingham City fan Deeney scored a penalty after he was barged over by Douglas Luiz, and Sarr slid in from Etienne Capoue's cross - a goal allowed after a VAR check for a possible foul in the build-up.
A much-changed Leicester deservedly won 2-1 at West Ham, who sacked manager Manuel Pellegrini less than two hours after full-time.
West Ham keeper Lukasz Fabianski conceded a penalty on his return to the team, but saved Demarai Gray's spot-kick.
Kelechi Iheanacho headed Leicester ahead but Pablo Fornals swept Felipe Anderson's cross first time past Kasper Schmeichel to equalise.
Gray made amends to score the winner for Leicester, who are 10 points behind Liverpool, as he clipped home from Ayoze Perez's pass.
In the day's final game, Manchester United climbed to fifth in the table as goals from Anthony Martial and Marcus Rashford earned them all three points at Burnley.
Andreas Pereira capitalised on a mistake by Clarets defender Charlie Taylor before playing in Martial, who beat Nick Pope at the near post for his third goal in two games.
Rashford sealed the win when he rounded the Burnley goalkeeper in the final minute of second-half stoppage time.
The Premier League's bottom club Norwich drew 2-2 with Jose Mourinho's Tottenham in an incident-packed match at Carrow Road.
Mario Vrancic took advantage of bad defending to put Norwich ahead and Teemu Pukki had a second controversially disallowed by VAR for maybe the tightest offside decision yet in the Premier League.
Christian Eriksen levelled for Spurs with a fine free-kick but Norwich went ahead again when Toby Alderweireld's clearance hit Spurs team-mate Serge Aurier and flew into his own net.
Harry Kane rescued a point for Spurs with a penalty after he had been fouled by Christoph Zimmermann.
Everton made it two wins from two under Carlo Ancelotti as they beat Newcastle 2-1 thanks to two Dominic Calvert-Lewin goals.
The striker prodded home from six yards out from Gylfi Sigurdsson's ball.
Newcastle's Miguel Almiron hit the post, and Andy Carroll had a goal disallowed for offside from the rebound. The striker set up their equaliser, heading across to Fabian Schar to volley home.
But Calvert-Lewin scored the winner as he slid in Richarlison's cross at the back post.
In the lunchtime game, Alireza Jahanbakhsh and Aaron Mooy scored their first Brighton goals in a 2-0 win over relegation rivals Bournemouth.
Jahanbakhsh, who was making his 27th appearance across 18 months, lashed home from Neal Maupay's lay-off. Mooy scored a classy second from Leandro Trossard's cross.
Bournemouth were very poor and Brighton should have won by more, with Dan Burn having a goal disallowed for offside and Yves Bissouma striking the post.
Crystal Palace and Southampton drew 1-1.
Max Meyer thought he put Palace ahead, but Wilfried Zaha was flagged offside for his role in the goal. They eventually led through James Tomkins' header from Luka Milivojevic's free-kick.
But in-form Danny Ings pounced on a defensive mistake to equalise for Southampton.