With the Red Devils level on points but behind on goal difference with their cross-town rivals the emphasis was on an emphatic victory, with Paul Scholes and Ashley Young scoring in the first half.
However, the champions could not add to their tally in the second 45, and are now dependent on QPR getting something from their game against City at the Etihad Stadium on the last day.
Despite being underdogs to lift the crown, Sir Alex Ferguson is refusing to give up hope.
“We have to go there with the right spirit to win the match. You never know,” he told Sky Sports.
“Our responsibility next week is to win the game.
“We’ve got next week. QPR need a point, so you never know. I just wish Sparky (QPR boss Mark Hughes) was playing,” he stated.
In regards to the victory over Swansea, the Scottish trainer felt his team played well and were good value for their win.
“We did what had to do. We won the match. We had a lot of chances. I thought we played very, very well.
“I was pleased to win the match,” he concluded.
By Gareth McKnight