The Red Devils put up another spectacular second half show to secure the maximum points at the Villa Park to make Premier League leaders Manchester City wait to be crowned champions.
Aston Villa took the lead on 24 minutes courtesy of Bertrand Traore but Manchester United pulled parity when Bruno Fernandes scored from the penalty spot ten minutes after the break.
Mason Greenwood got the visitors’ second goal moments later with a sublime finish before Edinson Cavani sealed Ole Gunnar Solskjaer’s men’s victory in the dying embers of the game.
Manchester United have now won 31 points from losing positions; the most of any Premier League side, but Shaw has warned his team-mates to always start stronger.
“Going 1-0 down in the first half we knew it was going to be a hard game and we have been in this situation so many times - second half we came back much better,” the England international said.
"That's a positive but we need to start the first half better than we normally do. Maybe we're not ready for the game but we have the quality and can't keep counting on second-half performances.
"He (Solskjaer) said exactly what I have just said, we have been in this situation a lot of times, we have the quality, are a fit team and we always believe. When we got the first goal I felt we were going to win.
"We are just focusing on ourselves, even more so we look at the City result and we are disappointed with the points we have let go this season. We have two games in four days, we need to be ready."