Beaten by Crystal Palace on the opening weekend of the Premier League season and crushed 6-1 by Tottenham in their previous home match, United once again looked lacklustre at an empty Old Trafford.
Chelsea had conceded 63 goals in their previous 43 Premier League matches under Lampard, the worst rate of any permanent Blues boss.
Solskjaer changed United's pre-match routine in a bid to arrest their Old Trafford slide, taking them to stay in a hotel on Friday night.
With torrential rain lashing down, nearly 30 minutes passed without a single notable incident before Chelsea keeper Edouard Mendy nearly scored an incredible own goal when his miscued pass across his six-yard box rolled just wide for a United corner.
Marcus Rashford had the best chance of the half when Juan Mata's pinpoint pass sent the United forward galloping clear for a low drive that forced Mendy to save with his foot.
Solskjaer made his move when he sent on former PSG star Cavani in the 58th minute for his first appearance since his free transfer on deadline day.