But they could have no complaints about the result as they looked way off the pace in their first match of the new campaign, little over a month since they ended the last one with defeat to Sevilla in the Europa League semi-finals.
Solskjaer kept faith with De Gea in goal ahead of Dean Henderson, who has returned to Old Trafford from an impressive loan spell at Sheffield United.
De Gea justified his inclusion even before the penalty save with a brilliant stop from Ayew in first-half stoppage time to keep the Red Devils in the game.
The Ivorian's first goal of the afternoon was ruled out by the offside flag from another promising Palace counter-attack.
Zaha took over the responsibility and this time crashed the ball home to score against his former club.