United won 2-0 at home to Everton on Super Sunday, with Ryan Giggs (13) giving the Old Trafford brood the lead, to preserve his record of netting in every Premier League season, and Robin van Persie doubling the tally just before half time.
The triumph over the Toffees, coupled with Man City's 3-1 reverse at Southampton on Saturday evening, has made Sir Alex Ferguson's troop overwhelming favourites to lift a 20th top-flight crown.
And former Old Trafford midfielder Wilkins told Sky Sports HD that the endeavour of the club's players and the passion of their manager will ensure that United seize league silverware in May.
"Mathematics always creeps into it, but the desire and work-ethic they have, which is what beat a dogged Everton side, should pull them through," Wilkins said of United, who squandered an eight-point lead with six games remaining of last term to see themselves overhauled by City.
"They are a very talented group of guys but when they graft like that it makes it very difficult for the opposition - and Sir Alex really wants to wrestle the title back.
"He doesn't want the guys across the road to be the kingpins and, for that reason, I think he classed this game against Everton as more important than the Real Madrid game on Wednesday, though that will be a classic encounter."
Former Man City and Everton manager Joe Royle says Ferguson's charges did not dazzle against David Moyes' side, who earned a 4-4 draw at Old Trafford last April.
But praised the game-plan of United - who lost to the Merseysiders in their opening game of the Premier League season at Goodison Park - and 'difference maker' Van Persie.
"United showed tactical nous," said Royle.
"They nullified Marouane Fellaini, who has been a thorn in their side in the past, and Antonio Valencia stopped Leighton Baines coming forward - though Everton were hamstrung not having Sylvain Distin fit to play.
"United weren't sparkling but they were more than effective and Van Persie, as I thought he would be before kick-off, was the difference; he scored one, hit the post and made a goal, and while he was often on the shoulder of defenders, he also came short.
"He has been the difference all season for United who now, with their goal difference, are virtually 13 points ahead of City and have the luxury of being able to bring on substitutes who don't weaken them.
"The title race is not over but it looks tough for City."
Everton, meanwhile, now lie six points behind fourth-placed Tottenham, but both Royle and Wilkins believe the Toffees are capable of securing a Champions League berth for next season.
However, Wilkins says there will be plenty of drama between now and the end of the campaign and is refusing to rule out Swansea's hopes of earning a spot in Europe's elite club competition.
"Everton's first XI is a top-four side, but they have to keep everyone fit and get their frontmen scoring," added Royle, who managed the Blues between 1994-97.
"Their strikers didn't give then a great deal against United; Victor Anichebe has been having a great time but he couldn't get going, while Nikica Jelavic was a Johnny-on-the-spot last year but it hasn't happened for him this season."
Wilkins added: "I've always fancied Everton to go the whole hog because David (Moyes) preaches to them that they have to keep going, but you cannot write Swansea off.
"They are a good deal of points away from fourth (11) but they are playing some wonderful football and could get in - but there will be lots of twists and turns."