United came from behind to draw 1-1 at Birmingham while Arsenal rescued a point when a last-gasp Tomas Rosicky equaliser earned a 2-2 home draw with Everton.
The results left Chelsea, who had their match at Hull City postponed because of the icy weather, clear at the top with 45 points from 20 matches followed by United with 44 from 21 and Arsenal with 42 from 20.
Tottenham Hotspur, who also had Sunday's trip to Liverpool called off, are fourth with 37 points from 20 games. The only other match due to go ahead is Manchester City's home game with Blackburn Rovers on Monday.
Manchester United, knocked out of the FA Cup last week by Leeds United, looked to be heading for another defeat at Birmingham. The home team, who set a club record by stretching their unbeaten run to 12 games, took the lead through Cameron Jerome after 39 minutes when United failed to clear a corner.
Birmingham more than matched the champions until Scott Dann conceded an own goal after 63 minutes when the visitors pressurised the City defence.
Manchester remained eighth, level on 33 points with Liverpool, but have played one more match.
At the Emirates, Rosicky's late goal saved Arsenal as the Londoners missed the chance to move within a point of Chelsea.
Czech substitute Rosicky finished off a flowing move with a deflected shot after Steven Pienaar's superb breakaway goal 11 minutes earlier looked to have won it for Everton in a second-half snowstorm. Arsenal had won four and drawn one of their last five league games and crushed Everton 6-1 at Goodison Park on the opening day of the season.