January signing Bruno Fernandes gave Ole Gunnar Solskjaer’s men the lead with his first goal for the club, converting a penalty he had won after being fouled by Ben Foster three minutes before half-time.
Anthony Martial got the second goal for the hosts after keeping his composure to dink the ball over Foster midway through the second half.
Fernandes then set up Manchester United academy graduate Mason Greenwood, who delivered the coup de grace for the Red Devils 15 minutes from time.
In an interview with Sky Sports after the game, Shaw admitted they have missed playing in the Champions League, and they will do everything to get back to the big stage.
"We got what we needed and that was three points. Let's keep pushing,” the former Southampton man said.
"The most important thing is we closed the gap to Chelsea.”
"This club is known for playing in the big competitions. We all miss the Champions League nights so much, that is what we want next season.
"We need to fight and earn it."
Fernandes capped a man-of-the-match performance with a goal and assist, and the Portuguese insisted every footballer relishes a day like this.
"This is the day every player wants to have,” the 25-year-old said.
“I feel lucky to score, I feel lucky to win the game. We all gave our best and we all deserved the win. I just need to help the team, it’s what I want to do, and it’s what I need to do.”
“I hope Martial scores more goals too like he did tonight."
