United boss Erik ten Hag and his players have been under fire after a disappointing start to the season.
But, following Saturday's narrow Premier League victory at Burnley, they secured a second successive win to ease the pressure at least a little.
When United lifted the League Cup in February to end a six-year trophy drought, it was seen as the start of a new era of success at Old Trafford.
Instead, United have been engulfed by a series of problems on and off the pitch.
Having lost three of their first five league games to severely damage their title hopes, Ten Hag was under mounting scrutiny until the last four days offered a ray of hope.
Ten Hag made a point of applauding the crowd and waving to all corners of Old Trafford before kick-off, setting the tone for an uplifting evening as his decision to make seven changes paid off.
Henderson's replacement Sam Johnstone had to pick the ball out of the net moments after coming on as United took a 21st minute lead.
Diogo Dalot's cross arrowed towards Garnacho and the Argentine winger swivelled to fire a low strike past Johnstone from 10 yards.
Casemiro increased United's advantage six minutes later, climbing highest to meet Mason Mount's corner with a glancing header that gave Johnstone no chance.
United's third arrived in the 55th minute when Martial rifled home from Casemiro's cross.
Giving further encouragement to Ten Hag, Morocco's Sofyan Amrabat impressed on his first start since his deadline-day loan switch from Fiorentina.
Amrabat lined up a stand-in left-back role before switching to his preferred central midfield position after half-time.
United will look to extend their winning run when Palace return to Old Trafford in the league on Saturday.