Papiss Cisse came closest to breaking the deadlock on an afternoon of few clear-cut opportunities, with the Senegal international seeing a first-half effort cleared off the line by Winston Reid.
Wigan's annual role as the Barclays Premier League escape artists was reprised again as they won 3-2 at West Brom.
Time and again Roberto Martinez's men have ended the season strongly to stay up, but going into Saturday's meeting five points shy of the rest, they looked in trouble.
That situation didn't improve when Shane Long tucked in Markus Rosenberg's cross for the Baggies, but Arouna Kone levelled before the break.
Gareth McAuley put West Brom ahead again five minutes after the restart but Wigan equalised through James McArthur (58) and won it when Callum McManaman scored with 10 minutes left.
The Latics now have 35 points, three less than Norwich whose dismal 2013 continued as they were beaten 2-1 by Aston Villa.
Gabriel Agbonlahor scored both goals for the visitors, who ensured Paul Lambert enjoyed a happy return to his old club.
Grant Holt netted a penalty to make it 1-1, but Norwich are now in trouble, compared to Villa whose two wins in a week have pushed them out to 40 points.
Tottenham enjoyed a good day in the race for a top-four place as they beat Southampton 1-0.
Spurs were struggling to find a goal at White Hart Lane until Gareth Bale unleashed a stinging 20-yard winner to keep Andre Villas-Boas' side battling it out with Arsenal and Chelsea.
Theo Walcott struck his 20th goal of the season after 20 seconds as Arsenal beat relegated QPR 1-0 in the late game to move back above Spurs to third place.
Arsenal's quickest Premier League goal and the swiftest of the season secured Arsene Wenger's side a straightforward win over hapless QPR, who are now without a goal in four games and six hours.
Loic Remy was denied by a fine Wojciech Szczesny save as the Gunners held on for a fifth successive away win saw to move two points clear of Chelsea, having played two games more, and Tottenham, who play at Stamford Bridge on Wednesday.
1 Man Utd 85
2 Man City 72
3 Arsenal 67
4 Chelsea 65
5 Tottenham 65
6 Everton 59
7 Liverpool 54
8 West Brom 48
9 Swansea 43
10 West Ham 43
11 Stoke City 40
12 Fulham 40
13 A Villa 40
14 Southampton 39
15 Norwich 38
16 Newcastle 38
17 Sunderland 37
18 Wigan 35
19 Reading 28
20 QPR 25
Already relegated Reading went goal crazy at Fulham, winning 4-2.
Hal Robson-Kanu's early penalty put the Royals on their way to giving Nigel Adkins his first win in charge, with the Wales international doubling his tally (62).
Bryan Ruiz gave Fulham a lifeline eight minutes later but Adam Le Fondre replied and, even though Ruiz scored again (77), Jem Karacan wrapped things up for Reading.
There was no such drama at Swansea, though, as the Capital One Cup winners played out a meek draw with Manchester City.
Swansea, who are now without a win in seven games, enjoyed the better of the opening half but were aggrieved that Cheshire official Jones opted not to award them a penalty when Matija Nastasic clattered into Michu.
City wasted two wonderful chances to claim the three points through Edin Dzeko and David Silva, adding to their frustration after Jones turned away appeals when the Bosnian went over Chico Flores just inside the box.