The home side had the better chances against a listless United but their failure to win left Chelsea top on 57 points, one clear of Arsenal with 12 matches to play.
Manchester City stayed third on 54 points and have a game in hand after their home fixture with Sunderland was postponed because of dangerously strong winds.
Liverpool are fourth on 53 points, a Steven Gerrard penalty in stoppage time giving them a 3-2 win at bottom of the table Fulham who twice led.
Tottenham Hotspur are fifth, three points behind Liverpool, after a superb 4-0 win at Newcastle United following two goals from Emmanuel Adebayor and one each by Paulinho and Nacer Chadli.
In the other match to survive the weather Stoke City drew 1-1 with Swansea City at the Britannia Stadium.
The storms battering Britain not only claimed Manchester City's game but also Everton's clash with Crystal Palace at Goodison Park.