Marcus Rashford gave United the lead from the penalty spot midway through the first half before Anthony Martial doubled it after half-time.
Rashford got his second moments later before Daniel James added a debut goal to cap off a heavy defeat for Lampard.
With Harry Maguire and Aaron Wan-Bissaka making their competitive debuts, Ole opted to field Andreas Pereira centrally behind main striker Martial, with Rashford on the left and Jesse Lingard on the right.
The visitors settled quickly and were unlucky not to be ahead within four minutes when Tammy Abraham turned to thud a loose ball against the woodwork with a truly hit strike that had David De Gea beaten. Pedro fired over seconds later but Martial should have done better at the other end, when presented with the ball by Kurt Zouma's sloppy pass, with Kepa Arrizabalaga saving the tame effort.
Chelsea continued to threaten with a dangerous cross by Cesar Azpilicueta and a drive by Mason Mount that De Gea stopped, but the key moment of the first half arrived when referee Anthony Taylor played an advantage as Andreas was fouled in midfield, before pointing to the spot when Rashford was up-ended by Zouma inside the box. As will be the norm, the decision was checked by VAR before being confirmed, and Rashford kept his nerve to drill past Kepa, even if the keeper guessed correctly by diving to his right.
