The Hammers went behind after only ten minutes when Craig Dawson headed home Craig Gardeners free kick.
It took the Hammers a while to get going but once they found fluency with their passing they started to take control of the game.
The equaliser came on 34 minutes when Andy Carroll volleyed Stewart Downing’s free-kick straight at Ben Foster and club Captain Kevin Nolan was on hand to knock home the rebound.
Just before the interval, James Tomkins rose highest from a Downing corner to head the Hammers into a half-time lead.
After the break both teams had their chances but the Hammers held-on well to secure their second victory on the spin to ensure they remain in 5th place in the Premier League table.