The Hammers made a nightmare start when Jonathan Spector headed Ben Watson's corner into his own net.
Ben Watson forced a low save from Foster with the resulting free-kick, but a draw was a fair result.
Ben Watson scored from the penalty and just two minutes later Victor Moses made it 2-0 for the hosts.
Wigan went ahead when Charles N'Zogbia was tripped by Laurent Koscielny in the box and Ben Watson scored the penalty.
The winning goal came from substitute Ben Watson off a corner kick directly in front of the 23, 000 or so Wigan fans here.
Carey fouled Jose Fonte and Ben Watson smashed in the penalty to level but Noble produced a sensational 30-yard effort to give City the advantage.
Nick Carle demonstrated his side's determination with two tough challenges in quick succession, but he was lucky to get away his first, a nasty one on Ben Watson.
Ben Watson scored on a header off Shaun Maloney's corner kick in the 90th minute at Wembley Stadium, six minutes after City defender Pablo Zabaleta was given a red card.
When fleeting opportunities did fall the home side's way, Fellaini headed over and a Jack Rodwell nod towards goal was diverted above his own goal by Wigan midfielder Ben Watson.
Moses could have had a second minutes later when he mis-kicked with the goal gaping after Maynor Figueroa knocked Ben Watson's cross into his path, but instead Hull were quickly level.
But while Palace had the fist sight on goal - a Ben Watson shot that sailed over - it was soon clear they would not have an easy task against a combative City side.
CNN's Ben Brumfield, Ivan Watson, Laura Smith-Spark, Joe Sterling and Chelsea Carter contributed to this report.
CNN's Ivan Watson and Ben Wedeman contributed to this report.
But if Woods and McIlroy are to become truly great adversaries along the lines of Nicklaus-Tom Watson and Ben Hogan-Sam Snead then they can't afford to become too cosy, according to sports leadership expert Khoi Tu.
Though Ponting, Gilchrist and Hayden remain, and dynamic fast bowler Brett Lee has returned, Nielsen will look to the likes of all-rounder Shane Watson and young paceman Ben Hilfenhaus to step up a level.
CNN's Amir Ahmed, Kareem Khadder, Ben Wedeman, Salma Abdelaziz, Ivan Watson, Hamdi Alkhshali, Yesim Comert and Joe Sterling contributed to this report.
The 23-year-old flanker follows Saracens number eight Ben Skirving and Western Province back-rower Luke Watson in moving to the Rec.
The American ended on 286 in a group including British Open runner-up Adam Scott of Australia, Masters champion Bubba Watson, 2010 U.S. Open champion Graeme McDowell and fellow former major winners Geoff Ogilvy and Ben Curtis.
CNN: New No. 1 McIlroy wins PGA Championship by record margin
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