But it proved to be a bitter-sweet day for the reigning champions, who will start as significant underdogs to clinch an unprecedented 20th title as rivals Manchester City close in on their first top-flight crown since 1968.
First-half goals from Paul Scholes and Ashley Young saw Sir Alex Ferguson's side draw level on points with City at the top of the table, but with a vastly inferior goal difference.
United kept the destiny of the Premier League trophy in doubt until the final round of games on May 13, but having surrendered an eight-point advantage, that promises to be scant reward for Ferguson's men.
To end the campaign, Manchester United travel to Sunderland, who have not beaten them in the league for 15 years, spanning 19 attempts.
However, City will be overwhelming favourites to beat a relegation-threatened Queens Park Rangers side who have won just three times on the road this season.
The Premier League title has never yet been decided on goal difference, but there is every chance this season that it will.
United will have to better City's final day result to finish above their near neighbours.
Victories for both -- barring a mathematical miracle courtesy of an unlikely nine-goal swing -- will spark huge celebrations in the blue half of Manchester.
United kicked off knowing two goals from Yaya Toure had seen City cement their grip on the title with a 2-0 win at Newcastle United earlier in the day.
Asked shortly before the start if City had a hand on the title, Ferguson replied: "Probably two."
Swansea's Michel Vorm was by far the busier of the goalkeepers, and the Dutchman was forced into a fine double save to deny Patrice Evra from 20 yards, and then a close-range follow-up from Wayne Rooney.
Michael Carrick was at the heart of things as the hosts finally broke the deadlock in the 28th minute.
Antonio Valencia beat Neil Taylor to make strides down the right before pulling the ball back for the lurking Carrick, who quickly re-directed the ball into the six-yard box.
Swansea had plenty of bodies back to cover, but that failed to prevent Scholes from reacting first to open the scoring with a close-range flick.
The lack of celebration from the veteran midfielder to meet his fourth goal of the season betrayed the true feeling in the United camp, one that their chase was a forlorn one.
United's second goal arrived four minutes before the break.
Swansea were made to pay for being caught in possession as they attempted to pass out of their own area, Scholes winning the ball to square for Rooney in the penalty box.
The England forward's snap-shot was blocked, but fell invitingly for Young to curl his eighth goal of the season into the bottom-right corner with a calm right-foot finish from 15 yards.
Rooney wasted a clear opening to claim a career-best 27th Premier League goal of the season after being released by Carrick as Welsh club Swansea were again carved open in ruthless fashion.
Having already secured another season in the top flight, Swansea rarely looked like improving on a dire record at Old Trafford that now sees them without a victory there in nine visits.
Nathan Dyer curled an early long-range effort narrowly over, and David de Gea made a meal of a low 25-yard shot from Gylfi Sigurdsson, before the Spaniard made amends with a fine save to deny Danny Graham from close range after the break.
When De Gea clawed out Sigurdsson's long-range free-kick shortly after Dyer blazed high and wide from a promising position, the last chance of mounting an improbable comeback had gone.
Defeat left Swansea in 12th place, with only one victory in their last eight league matches going into their final game at home to Liverpool.
Source: AFP
Source: AFP