Despite the result, the Red Devils were much improved and came close in the first half, when Juan Mata hit the crossbar and Anthony Martial saw his shot rebound off the post.
Chelsea had chances of their own in an entertaining game at Old Trafford, with Nemanja Matic coming closest for the visitors when he blazed over after finding himself through on goal in the second half.
The result left United in sixth place in the Premier League table and five points behind fourth-placed Manchester City.
Chelsea, meanwhile, are 14th in the table and just three points above the relegation zone after 19 games.
Monday evening’s big game at Old Trafford inevitably prompted plenty of activity on Twitter – and here are some of our favourite updates as the action unfolded at United’s home ground.
Best I've seen United all season- passing & team play outstanding – at the races
— Rodney Marsh (@RodneyMarsh10) December 28, 2015
— Mario Melchiot (@MarioMelchiot) December 28, 2015
United much better team that half…the ref has been lenient on the amount of cynical fouls from United though..
— Jody Morris (@morriskid) December 28, 2015
David de Gea is so good he could save Van Gaal.
— Gary Lineker (@GaryLineker) December 28, 2015
Bellerin stripping Bournemouth to pieces with his pace, but his final ball's been poor. So quick though. #afc
— Piers Morgan (@piersmorgan) December 28, 2015
Oh my goodness matic
— Matt Le Tissier (@mattletiss7) December 28, 2015
What a miss…!!!!
— Peter Schmeichel (@Pschmeichel1) December 28, 2015
I just lobbed on Sportlobster: https://t.co/hv9Sr3rwR7 No wonder these two teams are struggling. Poor game.
— michael owen (@themichaelowen) December 28, 2015
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