Arsenal beat Bournemouth 2-0 with goals from Gabriel and Mesut Ozil to move on to 39 points from 19 Premier League games, one ahead of Leicester City who are at home to Manchester City, in fourth, on Tuesday.
Dutchman Van Gaal, whose tenure in the Old Trafford hot seat is under intense scrutiny after a Champions League exit and three successive league defeats, was afforded a warm reception by fans who have been critical of his team’s lack of flair.
United responded with attacking intent, striking the woodwork twice in the opening 16 minutes and both sides created good chances throughout.
Chelsea, playing their second game under interim manager Guus Hiddink after Jose Mourinho’s sacking, wasted the game’s best opportunity midway through the second half when Nemanja Matic raced clean through before blazing the ball wildly over.
United, now eight games without a win in all competitions, are sixth on 30 points while Chelsea are 14th on 20.
Earlier, Tottenham Hotspur rose to third after Son Heung-Min netted a late goal in a 2-1 victory at 10-man Watford while Marko Arnautovic’s stoppage-time penalty gave Stoke City a 4-3 win at Everton.
Darren Fletcher’s 78th-minute goal for West Bromwich Albion was enough to beat struggling Newcastle United 1-0 while Aston Villa’s miserable season continued with the bottom side, marooned on eight points, going down 2-0 at Norwich City.
Crystal Palace and Swansea City drew 0-0.