The home side made the best possible start to the match courtesy of a strike from Michael Chopra after three minutes. The former Cardiff man collected a pass from Jay Emmanuel-Thomas before firing home from inside the area.
Chances were few and far between in the opening period before a stunning final five minutes of the half saw three goals scored.
Jack Collison cut the score to 2-1 with a thumping header from inside the area moments before the break, but when West Ham's George McCarthy fouled Chopra in the area, Lee Martin put his penalty away to extend the home side's lead to 3-1.
Emmanuel-Thomas had a wonderful chance to extend the home side's lead moments into the second period but fired just wide. He did not have to wait long to make amends, however, as he extended Ipswich's lead to 4-1 after 64 minutes.
It was five for the home side moments before the end, however, when Emmanuel-Thomas grabbed his second of the night with a cool finish inside the area.
Ipswich will look to continue their winning run against Coventry on Saturday, while West Ham host Millwall.