The visitors had the first chance of the match in the third minute and it fell to Antolin Alcaraz, who shot on target from 20 yards. However, Hammers goalkeeper Jussi Jaaskelainen made no mistake in keeping it out.
Jaaskelainen came to West Ham's rescue soon after, denying Shaun Maloney with a point-blank save after finding himself in an one-on-one situation with the Wigan forward.
Maloney had another crack on the London side's goal on 17 minutes when he stepped up to take a free kick from 20 yards, but his effort went narrowly over the crossbar.
Four minutes later West Ham took the lead when Matthew Jarvis controlled Joey O'Brien's pass on the left and whipped in a cross into the Latics penalty box that evaded everyone and nestled into the net.
Gary O'Neil failed to make it 2-0 to Sam Allardyce's side on the half-hour mark when he saw his attempt from long range saved by Joel Robles, and his teammates Andy Carroll, Ricardo Vaz Te and O'Brien did not do better with their chances in the remainder of the first half.