This was the sternest test of its resurgence under Ten Hag, even with City coming off a surprise 2-0 loss to Southampton in the English League Cup on Wednesday.
United had the better chances in the first half, with Rashford having one shot cleared off the line by Manuel Akanji after rounding Ederson and then seeing another effort smothered by the City goalkeeper.
City took control after the break and Grealish opened the scoring in the 60th minute, just three minutes after coming on, when he headed in Kevin de Bruyne's cross.
United evened the score against the run of play when Fernandes struck in the 78th minute.
The goal was initially ruled out by the referee's assistant because Rashford was in an offside position. However, that decision was overruled by VAR after it was confirmed the United forward did not touch the ball before Fernandes struck.
Rashford then hit the winner from close range just four minutes later when he converted substitute Alejandro Garnacho's cross.