Maxence Lacroix opened the scoring at Old Trafford after just four minutes but Bruno Fernandes leveled from the penalty spot on 57 minutes in an incident that saw Lacroix dismissed with a straight red, before Benjamin Sesko completed the comeback with goal on 65 minutes.
It was a second win in two games for Utd, following Monday's hard-fought 1-0 win over Everton, after their 1-1 draw with West Ham that interrupted a four-match winning run.
But this result sees Michael Carrick unbeaten in his seven games in charge, to leave the club in third place on the league standings with 51 points from 28 games, eight behind Manchester City and 10 adrift of leaders Arsenal.
Palace are down in 14th place with 35 points from 28 matches played.
Carrick will have been disappointed with the manner of the first goal as his men fell behind early on when Lacroix's looping header beat Senne Lammens.
United were kept penned in by the Eagles throughout the first half, before they were awarded a penalty.
Lacroix was dismissed after VAR review, for a foul on Matheus Cunha as he raced through on goal.
Benjamin Sesko was handed his first start since the 2-2 draw against Burnley and put United ahead from Fernandes' brilliant delivery to continue his fine goalscoring run. Sesko has scored six goals this season, including three in consecutive games.
Elsewhere, Tottenham suffered a disappointing 2-1 defeat away to Fulham at Craven Cottage on Sunday.
Former Spurs midfielder Harry Wilson opened the scoring for the home team after just seven minutes.
Alex Iwobi added a second with 34 minutes on the clock before a 66th minute consolation goal from Richarlison.
Interim Spurs boss Igor Tudor was in charge of just his second game following the 4-1 hammering by Arsenal, and now sees his team sit just four points above the relegation places, in 16th, with 29 points from 28 games.
It didn't take long for Spurs to find themselves trailing, as Wilson swept home his 10th league goal of the season.
Fulham doubled their lead in style as Iwobi played a one-two with Wilson on the edge of the box before firing in a shot off the post with the outside of his foot.
Calvin Bassey should have killed off the game for Marco Silva’s side but wasted a golden opportunity.
The home teeam ultimately saw out the result comfortably, with only substitute Richarlison netting - with his team’s first shot on target - the Brazilian rising highest to head home Archie Gray’s cross
Spurs have now conceded first in their last five Premier League outings and face a serious battle for survival, as Fulham chase their best Premier League finish since 2012, when they ended in ninth place.
Michael Carrick insists speculation linking Oliver Glasner with the Manchester United job will not add extra motivation when his side face Crystal Palace at Old Trafford on Sunday.
Manchester United have reported a sharp upturn in profitability despite declining revenues, with chief executive Omar Berrada citing the "positive financial impact" of the club's redundancy programme.
The UEFA Champions League round of 16 draw produced heavyweight clashes and high-stakes drama, with six Premier League clubs handed demanding tests on the road to Budapest.
Igor Tudor has admitted he was facing the biggest challenge of his managerial career as he attempted to steer Tottenham Hotspur away from the Premier League relegation zone.
