With the top four qualifying directly for next season's group stage, United are fourth in the table on 66 points, four ahead of fifth-placed Liverpool with both sides having three games left. Wolves are 13th on 40 points.
In a game played mainly at a sluggish pace, United's Brazilian winger Antony curled a shot wide in the ninth minute after sloppy Wolves defending, and he continued to offer a creative spark as he regularly cut in from the right wing onto his favoured left foot to shoot.
The 23-year-old headed over from point-blank range on the half-hour mark but he made amends two minute later, tearing down the right on a quick counter-attack and squaring the ball for Martial to fire home.
Antony was in the thick of the action again on the hour mark as Bruno Fernandes back-heeled the ball to him on the edge of the box, but the 23-year-old Brazilian's shot deflected just wide of the near post.
Fernandes should have made it two when he cut in from the left and fired from close range in the 64th minute but Wolves' debutant keeper Daniel Bentley saved his shot, and Jadon Sancho's similar effort was also kept out.
With the Wolves attack looking completely toothless, Casemiro forced another fine save from Bentley in the 82nd minute with a dipping shot, and substitute Wout Weghorst headed over the bar from close range from the resulting corner, but the second goal eventually came.
Brought off the bench in the 82nd minute after a long spell out due to an ankle injury, Garnacho wrapped up the three points with a long run and shot that bounced off the inside of the right-hand post deep into stoppage time to seal the win.
"We did our job, we needed to get the three points and win the game - after two defeats, we knew how important it was to get the momentum back to our side," United captain Fernandes said.
The Portuguese international praised 29-year-old Wolves keeper Bentley, who was playing his first Premier League game after a career spent at Southend, Brentford and Bristol City.
"We did a professional game and could have scored more, (but) their keeper had a really good game to keep Wolves in the game," Fernandes said.
"It wasn't a case of wasting our chances. Their keeper did a really good job, we have to compliment him."
