Martial had gone eight games without scoring before he netted in the first half at Old Trafford.
United's first win in three matches was wrapped up by Alejandro Garnacho's stoppage-time goal.
After successive defeats at Brighton and West Ham threatened to ruin their hopes of qualifying for the Champions League, Erik ten Hag's side restored order at Old Trafford.
Fourth-placed United, who sit behind Newcastle on goal difference, moved four points clear of Liverpool, who are fifth and play at struggling Leicester on Monday.
After that fixture, United will still have three matches left while Liverpool will have only two to play, leaving Ten Hag's men in control of their top four destiny.
Former manager Ole Gunnar Solskjaer was back at Old Trafford for the first time since being sacked in November 2021.
Solskjaer was all smiles as he took photos with fans before kick-off, but even the Norwegian's most ardent fan had to acknowledge the impressive progress made under Ten Hag this season underlined the failings of his own troubled reign.
Ten Hag made three changes as Marcus Rashford was sidelined by a leg injury, while Wout Weghorst and Tyrell Malacia dropped to the bench, with Martial, Jadon Sancho and Raphael Varane coming in.
United had scored only six times in their previous nine games, offering Liverpool renewed hope after six successive wins for Jurgen Klopp's team.
Wolves went close to snatching a shock lead when Craig Dawson fired just wide after Pedro Neto pulled the ball back to the defender inside the United area.
But Bruno Fernandes' free-kick forced a save from Wolves' rookie keeper Daniel Bentley as United's pressure gradually mounted.
The chances kept coming for United as Christian Eriksen whistled his strike just wide from long-range before Antony headed wastefully over from six yards.
Martial finally delivered in the 32nd minute as the French striker scored only his second league goal in 2023.
Fernandes' pass triggered Antony's incisive raid and when Bentley rashly came off his line the Brazilian unselfishly cut back to Martial, who finished with ease.
Martial could have doubled United's lead before half-time but he shot straight at Bentley from Antony's pass.
Wolves missed a good chance when Max Kilman headed a corner down to Hwang Hee-chan and the substitute screwed his shot wide from an acute angle.
Fernandes was unable to beat Bentley from close-range and the Wolves keeper made another good save to keep out Sancho's effort.
Weghorst, still waiting for his first Premier League goal for United, headed over from six yards.
Alejandro Garnacho then came off the bench to secure the points deep into stoppage time.
Newcastle and Manchester United are now four points clear of fifth-placed Liverpool with three games to go.
There was far more action at Elland Road where Leeds got a point but did not do enough to move out of the relegation zone.
Luke Ayling gave Allardyce's men a flying start, but they shot themselves in the foot three times.
Firstly, Patrick Bamford saw a penalty saved by Nick Pope.
Three minutes later, Newcastle did level from the spot through Callum Wilson after Alexander Isak was fouled.
Wilson converted a second penalty midway through the second half when Junior Firpo handled inside his own box.
Rasmus Kristensen's deflected effort brought Leeds level again 11 minutes from time.
But they were forced to see out stoppage time with 10 men after Firpo was shown his second yellow card.
"We missed a penalty, gave two away and drew 2-2," said Allardyce. "I think we'd be saying what a great three points if we scored that penalty for 2-0."
Leeds close to within one point of safety, but that gap could grow if Everton shock leaders Manchester City on Sunday.
Nottingham Forest remain three points clear of the relegation zone after their own four-goal thriller at Chelsea ended 2-2.
Taiwo Awoniyi's bullet header opened the scoring for the visitors.
Raheem Sterling's quickfire double turned the game around in seven second-half minutes.
But Awoniyi had the final say as he headed in once more from a long throw for his fourth goal in a week that could prove vital to keeping Forest up on their return to the top flight for the first time in 23 years.
Southampton's 11-year stay in the Premier League, though, is over after a meek 2-0 home defeat by Fulham summed up the Saints' season.
Carlos Vinicius and Aleksandar Mitrovic, on his return from an eight-game ban for pushing a referee, got the goals which moved Fulham up to ninth.
Defeat leaves Southampton still eight points adrift of safety with just two games remaining.
In the battle for a place in the Europa League next season, Aston Villa beat Tottenham 2-1 to move level on points with Spurs in sixth.
Jacob Ramsey gave Unai Emery's men an early lead and they were cruising to victory when Douglas Luiz curled home a free-kick 18 minutes from time.
Harry Kane's late penalty halved Tottenham's arrears, but their hopes of Champions League football next season are now mathematically over.
Eberechi Eze scored twice as Crystal Palace continued their revival under Roy Hodgson with a 2-0 win over Bournemouth.
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