With only three games remaining, United are one point adrift of the Blues following the dramatic, late derby victory over Manchester City.
A few hours later Chelsea failed to follow suit and lost to Tottenham at White Hart Lane.
United will go back to the top on Saturday should they beat a Spurs side aiming to claim a Champions League slot. Chelsea are not in action until the following day against Stoke.
Fletcher is delighted United have returned to winning ways after a difficult spell.
Sir Alex Ferguson's side exited the Champions League at the hands of Bayern Munich, as well as losing to Chelsea and drawing at Blackburn, which seemed to give their London rivals the advantage in the title.
Now it is too close to call at the top and Fletcher told Sky Sports News: "They are the team leading the league and all the pressure is on them. We are just taking care of ourselves.
"They were in a situation where they might have felt they could have pulled away and be in a real strong position but they are not.
"We never thought it had gone but is was a disappointing time after the Blackburn game. It was an uphill struggle but it just shows you in one weekend things can change."
Paul Scholes' stoppage-time winner in the derby not only gave United bragging rights but more importantly revived their bid for a record fourth successive crown.
Fletcher said: "Winning that game gave Tottenham something to play for and they did us a favour.
"We are a point behind now. All we can do is win our games. That's all we can do. Whatever happens happens.
"There have been some strange results all season. No one has really put a run together and that is credit to the league. The teams are getting stronger."