United trailed to Hugo Rodallega's first-half goal but the visitors surged back after the interval and now need a draw at home to Arsenal on Saturday to wrap up a record-equalling 18th crown.
NEWS: United set to seal title against Gunners
VIDEO: Wigan 1-2 Manchester United
The champions, who have won seven league matches in a row, have 86 points to second-placed Liverpool's 80 with two games remaining.
Tevez, who was quoted in Sunday's newspapers as saying he wanted to leave the club, came off the bench in the second half and produced a piece of magic after 62 minutes that left the 5,000 United fans in the stadium singing his name
"He is a fantastic little player," manager Alex Ferguson told Sky Sports. "He knows I want him to stay.
"I had a chat with him today, (chief executive) David Gill had some meetings today and I'm sure it's progressed further."
Tevez joined Dimitar Berbatov, Wayne Rooney and Cristiano Ronaldo in a four-pronged attack in the second half that finally wore down a spirited Wigan side.
United had to do it the hard way though after a poor first-half performance in which they were continually stretched by the movement of Antonio Valencia and Rodallega.
GOOD CHANCE
Valencia wasted a good chance in the opening minutes before Rooney squandered an opportunity at the other end.
Wigan went ahead after 29 minutes when Rodallega challenged Nemanja Vidic for a high ball and when it dropped to the floor he reacted quicker than the off-balance Serb to drill a shot inside Edwin van der Sar's near post.
Rooney blazed another effort over the bar while Rodallega almost made it 2-0 before halftime.
United were much better after the break especially after Tevez replaced Anderson in the 58th minute.
The Argentine had only been on the pitch four minutes when he flicked an off-target Carrick shot through his own legs with his back to goal, directing the ball beyond Wigan keeper Richard Kingson in a flash.
It was the signal for a United onslaught.
Ronaldo fired one effort high over the bar but was involved in the winner when his low cross arrived at Carrick's feet and the midfielder sent an unstoppable shot past Kingson.
"We just had to keep patient," said Ferguson, now on the verge of an 11th title with United. "It was a great second goal by Carrick and a really gutsy performance by us."
UNITED FANS! Check FourFourTwo.com’s ever-expandinginterviewsarchive for more stuff to read:
Web Exclusives Wayne Rooney, Peter Schmeichel, Carlos Tevez
Q&A Wayne Rooney, Cristiano Ronaldo, Ruud Van Nistlerooy
One on One David Beckham, George Best
