The Cottagers conceded inside eight minutes when Mo Diame slotted home before Steve Sidwell responded with a powerful header from a Damien Duff corner just after the half-hour mark.
Hammers skipper Kevin Nolan saw red before half-time for kicking out at Fernando Amorebieta prior to Dimitar Berbatov's eventual 66th-minute which saw the southwest London club move up to 16th, delighting manager Rene Meulensteen.
"We wanted to start in the best possible way with the best possible result," he told Sky Sports.
"We got three points and we deserved them and it was hard work still against 10 men but I am delighted for the players."
He added: "We didn't want Hull (6-0 loss on the weekend) to factor on today's performance - which it didn't - and six points in three games is good."
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