The 38-year-old former Chelsea striker scored in the 3-1 win over Gillingham and twice found the net in their 3-0 Carling Cup victory over Sunderland.
Furlong moved to Kenilworth Road during the summer after his release by QPR.
He beat Leeds' Jermaine Beckford for the award. The other contenders were Leyton Orient's Sean Thornton and Tranmere's Chris Greenacre.