Only Darren Fletcher retained his place from the team that had drawn with Everton three days earlier.
"It was difficult conditions and the pitch wasn't great, " Manchester United midfielder Darren Fletcher told Sky Sports.
And Brazilian full-back Rafael added a third after collecting Darren Fletcher's pass before drilling past goalkeeper Chris Kirkland.
"You have to accept big players and big stars move on at every club, " said midfielder Darren Fletcher.
However, There was a late sting in the tail for United when midfielder Darren Fletcher tackled Cesc Fabregas in the penalty area.
Midfielder's Michael Carrick and Darren Fletcher started at the back with full-back Patrice Evra, and were put under heavy pressure early on.
Players like Darren Fletcher, Stephen Pearson, Paul Gallagher and James McFadden have got time on their side - whether Vogts does is questionable...
Soon after, Darren Fletcher saw his curling 25-yard drive superbly tipped round the post by Green as the Red Devils continued to press.
Giggs was found by a Darren Fletcher ball from midfield and immediately curled in a ball for Rooney to slot past keeper Asmir Begovic.
Wenger was also unhappy with Dean's decision earlier in the match not to award his side a penalty for Darren Fletcher's untidy tackle on Arshavin.
Before that, Darren Fletcher and Ryan Giggs scored before the break.
Wayne Rooney met Darren Fletcher's cross to head the opener and the lead was doubled when Nani's low cross was deflected in by Anthony Vanden Borre.
Ferguson has already revealed his intention to play midfielder Michael Carrick in central defence while another midfielder, Darren Fletcher, seems certain to occupy a defensive berth too.
Scotland captain Darren Fletcher should have made it two on the stroke of half-time when he cut inside and shot over the top from only 12 yards.
Gary Naysmith then sent in a superb cross, but Darren Fletcher failed to connect from inside the six-yard box, much to the visible frustration of Burley on the touchline.
Soon after, Alcaraz was sent off for a foul on Darren Fletcher as he picked up his second booking of the match as Wigan's task became that much harder.
Macedonia goalkeeper Jane Nikolovski then let a tame Kenny Miller shot squirm from his grasp but a defender managed to get a toe to the ball ahead of the sliding Darren Fletcher.
And as United stepped up a gear after the interval, Darren Fletcher was only inches away from restoring their lead with a flashing shot from the edge of the area.
West Ham started confidently enough but it was the champions who had the first clear opportunity when Rooney squandered a great chance to open the scoring after Darren Fletcher's through-ball.
United are without Portuguese winger Nani and, most probably, Scottish midfielder Darren Fletcher after the pair suffered injuries in the club's 3-0 Champions League victory at Bursaspor on Tuesday.
BBC: Wayne Rooney to spend week in US to recover from injury
Rooney, who played with great conviction, collected a Darren Fletcher through ball just after the half-hour mark and shot across goal on the turn - his effort missing by inches.
United then held sway and snatched a deserved winner on the hour when Darren Fletcher's cross deep into the heart of the Liverpool penalty area was headed in by Ji-Sung Park.
Ryan Giggs took the place of the suspended Darren Fletcher in the United line-up - and for the first 10 minutes they penned a nervous Barcelona back in their own territory.
Darren Fletcher patrolled the midfield with purpose, Carrick picked passes for fun, Valencia was a constant nuisance down the right-hand side, while Rooney's performance will cause the Wigan defence nightmares for months.
The match at Stamford Bridge was decided by a 76th minute freekick awarded to Chelsea by referee Martin Atkinson who judged that Darren Fletcher had fouled Ashley Cole close to the touchline.
"Clearly, Darren Fletcher's won the ball, Ashley Cole's never touched and has jumped up in the air, and then (Didier) Drogba's pulled Brown to the ground for the goal, " Ferguson told reporters.
United's strikers, however, are yet to find the net after three matches of the new season, with Darren Fletcher scoring their only goals in both of the opening two Premier League fixtures.
Ronaldo added a second goal after the break, while a late Robin van Persie penalty for the Gunners - after Darren Fletcher was deemed to have fouled Cesc Fabregas - was little consolation for Wenger.
If the goal may have been in part down to Darren Fletcher's unfamiliarity with the right-back position, Agbonlahor is a familiar sight on the scoresheet against United, having notched against them in the last four season.
Ferguson could employ a makeshift centre-half pairing of midfielders Michael Carrick and Darren Fletcher as he waits for his walking wounded to return to fitness, although he is reportedly trying to convince Evra to switch to centre-half.
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