On another dramatic day in England's top-flight, United's hopes of continuing a promising unbeaten start to the campaign were undone by Palace's 93rd-minute strike from Patrick van Aanholt in a 2-1 victory for Roy Hodgson's strugglers.
Daniel James thought he had earned United a point by cancelling out Jordan Ayew's first-half goal in the 89th minute but United were left to rue their second missed penalty of the week.
After Paul Pogba had missed on Monday against Wolverhampton Wanderers, this time it was Marcus Rashford who spurned the opportunity, his shot hitting the inside of the post.
Lampard, back at the club he graced for 13 years as a player, fielded the youngest Chelsea side in a league match for 25 years with an average age of 24.
He was left delighted to see one of those young guns, 21-year-old Abraham, score his first goals for the club.
Abraham struck in just the third minute, and after Norwich had twice fought back from a goal down, he also proved the match-winner at Carrow Road with another superb strike in the 68th minute.
Another of Lampard's starlets, Mason Mount, also scored a fine goal while Teemu Pukki continued his dazzling start to the season for Norwich by netting a league-leading fifth goal. Watford saw their painful, pointless start to the season continue with a 3-1 defeat at Vicarage Road to West Ham United, for whom new record French signing Sebastien Haller scored a second-half double.