Lampard's side were on top for large patches but ended up being blown away at Old Trafford, where Rashford's double complemented goals from Anthony Martial and debutant Daniel James as United's curtain-raiser ended in a dream 4-0 victory.
Manchester United manager Ole Gunnar Solskjaer admitted his side had their moments of fortune throughout the contest, particularly in the first half.
Chelsea had the lion's share of possession and more shots at goal but were ultimately left reeling from their heaviest loss to United at Old Trafford since 1965.
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Two minutes later, Chelsea's defence was again exposed when Rashford timed his run to perfection, latched on to a long ball from Paul Pogba and beat keeper Kepa Arrizabalaga with a confident finish. They snapped into tackles, looked calm defensively and even though Chelsea caused United problems defensively, it was more so down to Luke Shaw and Victor Lindelof being caught out of position or sloppy passes in midfield. Little more than 12 months later, he was scoring on his Manchester United debut at a throbbing Old Trafford to put the ribbon on his new club's best result against Chelsea since 1960. We gave the ball away in unsafe areas.
Lampard bristled at those questioning his starting XI, insisting he was limited because of injuries to first-team personnel such as Antonio Rudiger and Willian, while a knee issue relegated N'Golo Kante to a cameo appearance. On this showing neither Zouma or Christensen did themselves any favors.
Pogba's early penalty got the ball rolling, and Luke Shaw added a second after the interval which proved to be enough to bring home the three points.
Head coach Lampard said: "We were clearly the better team for 45 to maybe 60 minutes".
After stating earlier this summer that he might be ready for a fresh challenge three years after his £89m record-breaking move to United in the summer of 2016, Real Madrid and Juventus have been heavily linked with a move for the French World Cup victor. He was booed and cheered when his name was read out over the PA announcer. "The performance in the second half was very pleasing, that was the big plus".