Despite an vastly improved performance by the Old Trafford side they were unable to break the deadlock against the visiting Blues and finished with a share of the points.
The result keeps United boss Louis Van Gaal’s future in serious doubt whilst it also left Chelsea’s interim coach Guus Hiddink hunting a first win since his return to the club for a second stint following the recent sacking of Jose Mourinho.
Arsenal, meanwhile, jumped back to the top of the table with a 2-0 win over Bournemouth.
Gabriel Paulista and an inspired Mesut Oezil did the damage for the Gunners at the Emirates as they now sit one point clear of Leicester, who play on Tuesday.
Manchester United are nine points behind in 6th while Chelsea move up to 14th but they remain only three points above the drop zone.