The first goal came after only 16 minutes as Carroll rose above Jonas Olsen to power home a header from a O’Neil corner.
O’Neil then got on the score-sheet himself, his first for the club, when he clipped an dipping effort over Ben Foster in the Baggies goal.
The Hammers dominated the game completely and even found a third goal in the 80th minute when Carroll produced a wonder-strike. Watching a long ball up-field from James Collins come down over his shoulder, he then hit a volley first time into the corner of the net.
The Hammers conceded a late penalty that was converted by Graham Dorrans but it proved only to be a consolation goal as the Hammers ran out 3-1 victors.