Ole Gunnar Solskjaer's side knew a Champions League spot was in their own hands if they could win all of their remaining games, including the final matchday against Leicester.
But now Manchester United also have the incentive of knowing they can move above Chelsea and Leicester into third with a win over Southampton.
It comes after Frank Lampard's Blues slumped to a 3-0 defeat against the Blades at Bramall Lane on Saturday evening and Bournemouth coming from behind to beat Leicester 4-1 at the Vitality Stadium last night.
Man United cantered past relegation-threatened Aston Villa at Villa Park on Thursday night, which extended their unbeaten run in all competitions to 17 matches and also saw them become the first team in Premier League history to win four games in a row by a margin of three or more goals.
Despite starting sluggishly, The Red Devils took the lead through Bruno Fernandes' controversially awarded penalty kick in the 27th minute, and after that, they never needed to get out of first gear.
It could have been a completely different story had Trézéguet's right-footed shot found the net instead of David De Gea's left-hand post just moments before Jonathan Moss had pointed to the spot to award United their 13th penalty of the season - equalling the Premier League record for spot-kicks awarded in one campaign.
Mason Greenwood's right-footed howitzer from 20 yards doubled United's advantage just before the interval and Paul Pogba's curling strike in the second half compounded more misery on Dean Smith's already deflated Villa side, who lost all of their belief when VAR chose not to overrule Moss' penalty kick decision.
However, they face a much sterner test in Southampton, who have come a long way from the humiliating 9-0 defeat to Leicester City at St Mary's earlier in the year.
Ralph Hasenhüttl has been getting the very best out of his counter-pressing, mid-table Southampton side who have had their Premier League status for another year secure for some time.
They could have been excused if their recent performance levels were not at the required standards since the restart, but that is simply not the case, as they have only lost once since #ProjectRestart'.
Hasenhüttl's side grabbed everyone's attention when they recorded a huge scalp by beating Manchester City 1-0 and they were unlucky not to take all three points against Everton at Goodison Park in their last game.
The Saints sit joint third in the current form table with Arsenal, Burnley and Liverpool - only Manchester United and Chelsea have accumulated more points.
Solskjaer named an unchanged lineup for the fourth consecutive Premier League game running and with no new injuries, the Manchester United boss could be tempted to name the same Starting XI once more.
Phil Jones and Axel Tuanzebe remain the only players unavailable for selection.
Hasenhüttl opted for the same team that beat Man City in their last game against Everton and with no new injuries, he too could name the same squad.
Long-term absentees Sofiane Boufal, Moussa Djenepo, Nathan Tella and Yann Valery remain sidelined, whilst it is touch and go whether Jannik Vestergaard will be fit enough to return to the squad.
Manchester United: De Gea, Shaw, Maguire, Lindelof, Wan-Bissaka, Matic, Pogba, Rashford, Fernandes, Greenwood, Martial. (4-2-3-1)
Southampton: McCarthy, Bertrand, Bednarek, Stephens, Walker-Peters, Redmond, Romeu, Ward-Prowse, Armstrong, Ings, Adams. (4-4-2)
Ones to watch
The young 18-year-old starlet has come on leaps and bounds since the hiatus and appears to have benefitted the most from the break, having netted four goals in the last three games - 16 overall for the season in all competitions.
In his last seven games, the right-sided attacker has recorded 15 shots, of which five have found the net (eight were on target).
Only George Best, Brian Kidd and Wayne Rooney - all with 17 goals have scored more as teenagers in one season for United.
Ings has continued his rich vein of goalscoring form and is The Saints' main threat having netted four times since the restart, which has taken his tally to 19 for the season.
He is now level on goals scored with Mohamad Salah and just three behind the current golden boot leader, Jamie Vardy with four games to play.
Prior to this season, he had only netted over ten goals once before, which came in the 2014-15 season for Burnley when he scored 11.
In what seems a lifetime ago, The Red Devils drew 1-1 with Southampton at St Mary's back at the end of August.
Vestergaard's towering header in the second half cancelled out Dan James' first-half opener, and despite piling on the pressure, United were unable to find the winning goal after Kevin Danso was sent off for a second bookable offence.
The result left Solskjaer's side with just one win from their opening four matches, which came on the opening matchday against Chelsea.
These two sides have met 41 times since the inception of the Premier League in 1992, of which United have won 20, lost 14 and drawn 7.
Southampton have only won twice at Old Trafford in that time - the last of which came on 23 Jan 2016 when Charlie Austin came off the bench to score in the 87th-minute goal on his debut.
Where to watch
The match kicks off at 20:00 (BST) on 13 July. Football fans in the UK will be able to watch the match live on Sky Sports Main Event and Sky Sports Premier League in Ultra HD + Sky One and Pick (Sky's free-to-air channel). Those in the United States will be able to watch the game live on NBC Sports Network.
Solskjaer spoke to the press at MUTV about the threat of Southampton:
He said: "Well, first of all, Southampton is a very fine football club with traditions. You can see it’s a proper football club.
"I wasn’t expecting any changes and I’ve followed Ralph’s time there and you know what he’s doing. I’ve got huge respect for the way they have turned it around.
"They have it, call it a German [Austrian], aggressive, rock-and-roll style of football. It’s direct, it’s high energy. It’s hard work but it’s difficult to play against.
"If you want to be a part of his team, you've got to be able to run 10, 11 or 12K. You've got to be able to sprint.
"We’ve watched quite a few games and I really enjoy watching them because it’s high entertainment and it’s high energy all the time.”
Hasenhüttl believes Southampton have become "more dimensional" since the restart and that his team can become an even better footballing side.
"I think we are now a more dimensional team," he said, speaking to the press at Southampton.
"We don’t only focus on our work against the ball – we need to have solutions against every opponent.
“If they give us more long balls to defend, we can do this; if they build up more, we can press; if they keep the ball well and we cannot get it back, we have to keep possession so we’re not always running without the ball.
“In every regard you must get better. In this moment it looks like we can make this step, and the players are open-minded to go this way.
“This is important, otherwise you will always stay on the same level.”