Guaita made excellent stops to deny Fernandes and Ronaldo in the first half as United controlled the game.
Telles hit the crossbar with a free-kick after the break, and Ayew fizzed a low drive from close range just wide.
The Red Devils have now gone four games without losing in all competitions, and they have moved up to sixth place in the rankings.
In the Champions League, they will face Young Boys next. Palace have now dropped to 12th place in the Premier League after losing their previous three games.
Next Saturday, they go to Everton, who are currently in relegation trouble.