Danny Welbeck returned from injury to maintain Arsenal's recent revival as the England striker sealed a 1-0 win at West Bromwich Albion, while struggling Liverpool got back on track with a 1-0 victory over Stoke on Saturday.
Arsene Wenger's Arsenal had been under pressure after successive Premier League defeats condemned them to their worst start for 30 years, but a midweek victory over Borussia Dortmund, which booked their place in the last 16 of the Champions League, had lifted spirits at the north London club.
Welbeck missed that win due to hamstring and knee problems, but he was back at the Hawthorns to net his sixth goal for Arsenal, ending a run of six club matches without a goal for the former Manchester United forward and giving the Gunners only their fifth league win of the season.
Welbeck won it on the hour when he met Santi Cazorla's cross with a powerful close-range header that Ben Foster could only help into the net.
Despite the win, at full-time some Arsenal fans held up a banner calling for Wenger to quit.
Asked if he was affected by the protest, Wenger said: "I don't want to comment on that. I try to do my best for this club that I love.
"We are very united with the players and staff around the team, that's all you can do.
"It's easier to deal with the upwards than the downwards, but you cannot be a manger and have only one side."
Liverpool ended their three-match losing streak as Glen Johnson's late goal clinched a hard-fought success against Stoke at Anfield.
Reds captain Steven Gerrard was dropped to the bench on the 16th anniversary of his Liverpool debut and Brendan Rodgers' side were lacklustre without him.
Stoke's Bojan Krkic hit the woodwork in the second half, but Liverpool improved after Gerrard came on for the final 16 minutes and England right-back Johnson popped up with the winner in the 85th minute after Rickie Lambert's header had hit the bar.
Robin van Persie scored only his fourth goal for Manchester United this season as the hosts cruised to a 3-0 win over Hull at Old Trafford.
United's injury problems continued early in the first half when Argentina midfielder Angel di Maria was forced to come off.
But Louis van Gaal's side took the lead in the 16th minute as video technology showed Chris Smalling's scrambled effort had crossed the line to give the much-maligned defender his first goal since December 2013.
United captain Wayne Rooney got the second goal, sweeping home from 20 yards in the 42nd minute, and van Persie netted in the 66th minute to seal his fourth-placed team's third successive win.
West Ham leapfrogged Newcastle into fifth place with a 1-0 win at Upton Park.
Newcastle had climbed into the top five on the back of five successive league victories, but they fell behind in the 56th minute when Hammers left-back Aaron Cresswell turned in Cheikhou Kouyate's miscued shot.
The Magpies' hopes of an equaliser were wrecked when midfielder Moussa Sissoko was sent off for earning two bookings in the space of 46 seconds in the second half.
QPR moved off the bottom of the table at the expense of fellow-strugglers Leicester, who slipped to 20th place after their 3-2 defeat at Loftus Road.
Leicester had gone 503 minutes without finding the back of the net before Esteban Cambiasso's low finish in the fourth minute.
QPR equalised thanks to Wes Morgan's 37th minute own goal before Dutch midfielder Leroy Fer put Harry Redknapp's team ahead with his first goal for the club on the stroke of half-time.
Leicester's Jeffrey Schlupp drove home a superb 67th minute equaliser, but Charlie Austin poked in the winner with 17 minutes remaining.
Burnley rescued a 1-1 draw against relegation rivals Aston Villa at Turf Moor.
Former Chelsea star Joe Cole marked his first start since December 2013 with the 38th minute opener for Villa, who are without a win in nine games.
But Danny Ings equalised with an 87th minute penalty to add to the pressure on Villa boss Paul Lambert following the resignation of his assistant Roy Keane earlier in the week.
Swansea and Crystal Palace drew 1-1 at the Liberty Stadium, with Wilfried Bony's 15th minute opener for the hosts cancelled out by a 25th minute penalty from Australia midfielder Mile Jedinak.