Antonio Valencia and Danny Welbeck got the goals within 14 minutes of the second half starting and midfielder Fletcher felt the win was a reward for a change of approach.
United midfielder Darren Fletcher said afterwards: "We raised the tempo in the second half.
"Swansea like to keep the ball and are one of the best teams in the league. There was a slight tactical change too, with Adnan Januzaj going out to the left and Shinji (Kagawa) in behind the striker.
"It worked and we went on to win the game."