But West Ham blew one chance of an equaliser and then found their luck was out when Alessandro Diamanti, who was making his debut, hit the post ten minutes from time.
England keeper Robert Green had shown his quality to deny Wigan an early lead producing an excellent save to keep out a tricky shot from midfielder Jordi Gomez after Jason Koumas created the opening.
Earlier the Latics survived a penalty appeal when 20-year-old striker Zavon Hines went crashing to the ground inside the area after a collision with Maynor Figueroa.
But ref Alan Wiley was well positioned and unimpressed by the Hammers' spot-kick claim.
Mohamed Diame then tried his luck from long range just missing the target by inches.
Keeper Chris Kirkland - back in the side after injury and keen to press his own World Cup claims - twice came to Wigan's rescue.
He did well to get down and turn away a shot from Junior Stanislas in the crowded goalmouth, and he was on red alert again to stop another from the lively Hines, fresh from a midweek hat-trick for the reserves.
Wigan threatened again when Scott Parker gave the ball away in midfield with a terrible pass but Green did his job tipping over the shot from Rodallega which took a deflection off Matthew Upson.
The Latics went close again when Gomez let fly from 20 yards, but Green moved neatly to his right to keep it out.
The Hammers did have the ball in the Wigan net when Carlton Cole beat Kirkland from a quickly taken free-kick harshly awarded against Hendry Thomas.
But Cole's celebration was cut short when he realised that ref Alan Wiley had already blown up for half-time.
The deadlock was finally broken when Rodallega gave Wigan the lead, scoring from six yards after the initial shot from Koumas was beaten out by Green after Mario Melchiot hammered the ball across goal.
West Ham missed a clear cut chance to level when James Tomkins headed wide from a Mark Noble corner. Then Kirkland came up trumps keeping one out from Parker.
Diamante then rattled the woodwork and when West Ham were caught on the break, Gomez fired wide.