New signing Bruno Fernandes opened his goal-scoring account for United at Old Trafford from the penalty spot.
Manchester United moved onto the shoulder of fourth-placed Chelsea on Sunday after brushing aside lowly Watford as Wolves and Arsenal also staked their claims for Champions League football next season.
With runaway leaders Liverpool looking certain to win the Premier League, attention has switched to the race for European places, with just 10 points separating fourth-placed Chelsea from Southampton, in 12th spot.
New signing Bruno Fernandes opened his goal-scoring account for United at Old Trafford from the penalty spot before impressive second-half goals from Anthony Martial and Mason Greenwood sealed a 3-0 win.
It means United, who have struggled to find consistency all season, are now in fifth place on 41 points, just three adrift of Chelsea.
United paid tribute to the late Harry Gregg, hero of the 1958 Munich air disaster, before kick-off at Old Trafford, where Fernandes calmed the nerves in a superb individual display.
Ole Gunnar Solskjaer praised his new signing, who picked up the man-of-the-match award for his display against Watford, languishing second from bottom of the table.
"He has done fantastic," said the Norwegian boss. "He has given everyone a boost. He wants the ball all the time, he wants to conduct the play.
"I am very pleased for him. He has done something to the crowd. He shows the attributes of a Manchester United player. He is a great addition to the squad."
Portugal midfielder Fernandes is under no illusions over his task as United look to return to the lucrative Champions League after a season away.
"Everyone knows we want to get into the Champions League places. I am here to help the team conquer this place and keep winning games," he told the BBC.
Wolves, in eighth place, are just two points behind United after a convincing 3-0 win against bottom-club Norwich at Molineux.
Diogo Jota scored twice and Raul Jimenez poached his 21st of the campaign early in the second period to leave Norwich seven points adrift of safety and looking doomed.
Wolves boss Nuno Espirito Santo said his side had managed the game well.
When asked about challenging for a Champions League spot, he said: "We're going to stay focused because the difficulty is to sustain your performances through the season.
"After that, we'll see, but it's about building your team and getting them ready to compete whenever, wherever."
- Arsenal comeback -
In the day's late kick-off, Arsenal recovered from a terrible start to hand Carlo Ancelotti's Everton their first Premier League defeat since New Year's Day.
Dominic Calvert-Lewin finished acrobatically after Arsenal failed to deal with a free-kick in the first minute.
Arsenal were level in the 27th minute when Eddie Nketiah finished expertly past Jordan Pickford from Bukayo Saka's cross and six minutes later they were ahead when Pierre-Emerick Aubameyang raced clear and finished coolly.
Everton equalised in first-half stoppage time when Richarlison got the faintest of touches to a header from Yerry Mina to poke past Bernd Leno but Arsenal retook the lead when Aubameyang scored his second moments after the re-start.
Arsenal survived a late scare to climb to ninth in the table, two points behind Wolves.
As it stands, fifth place could be enough to earn a Champions League spot because second-placed Manchester City have been banned from Europe's elite competition for two seasons, pending an appeal.
On Saturday, Chelsea strengthened their grip on a top-four place by beating London rivals Tottenham 2-1 on a day overshadowed by controversial VAR decisions.
Officials ruled that Spurs midfielder Giovani Lo Celso did not deserve to be sent off for a stamp on Cesar Azpilicueta that Chelsea boss Frank Lampard called a "leg breaker".
There were also incidents involving the technology in Bournemouth's defeat at Burnley and Manchester City's win at Leicester.
Elsewhere, there were wins for Crystal Palace and Southampton while high-flying Sheffield United drew 1-1 with Brighton.