Martial, who had gone eight games without finding the back of the net, ended his barren spell with a goal in the first half at Old Trafford. Alejandro Garnacho sealed United's first win in three matches with a stoppage-time goal.
Following consecutive defeats against Brighton and West Ham that jeopardized their chances of qualifying for the Champions League, Erik ten Hag's team restored order on their home turf.
Sitting in fourth place, Manchester United moved four points clear of fifth-placed Liverpool, who have a game in hand and were set to face struggling Leicester on Monday. With three matches remaining for United and only two for Liverpool, Ten Hag's men held their destiny in their own hands in the race for a top-four finish.
Former manager Ole Gunnar Solskjaer made a return to Old Trafford for the first time since his sacking in November 2021. While Solskjaer greeted fans and posed for photos with a smile, even his staunchest supporters had to acknowledge the significant progress made under Ten Hag this season, which highlighted the shortcomings of Solskjaer's troubled reign.
Ten Hag made three changes to his lineup, with Marcus Rashford sidelined due to a leg injury. Wout Weghorst and Tyrell Malacia were benched, making way for Martial, Jadon Sancho, and Raphael Varane.
United had struggled to find the net, scoring only six times in their previous nine games, giving Liverpool renewed hope after a run of six consecutive victories under Jurgen Klopp.
Wolves came close to taking a shock lead when Craig Dawson narrowly missed the target after Pedro Neto pulled the ball back to him inside the United area. However, Bruno Fernandes' free-kick forced a save from Wolves' young goalkeeper Daniel Bentley as United gradually built pressure.
United had several chances to extend their lead, with Christian Eriksen narrowly missing the target from long range, and Antony heading wastefully over from close range. Martial finally broke the deadlock in the 32nd minute, scoring his second league goal of 2023.