Blackburn immediately hit back as Scott Parker flicked a clearance on only for Vince Grella to intercept and head into the path of striker Roberts.
He turned Davenport and Behrami and poked home before the visitors were denied what appeared a legitimate equaliser.
Samba headed a free-kick into the path of Derbyshire, who turned the ball in but was ruled offside when he appeared level with the last defender.
But Rovers were given a great chance to level after the break when Steven Reid's free-kick was handled by Cole.
Roberts stepped up to take the penalty only to see Green dive to his left and save.
Curbishley hopes the result will boost confidence
Green quickly came out to force Derbyshire to lob an effort high and also saved a Brett Emerton header as the visitors pressed for an equaliser in an entertaining game.
At the other end, keeper Paul Robinson produced an even better save to turn a Cole shot round the post.
But he could do nothing when Bellamy raced clear and half-volleyed home in injury-time before Cole sidefooted in a cross to give the scoreline a more emphatic look than was warranted.
West Ham manager Alan Curbishley:
"I'm just delighted we got the win. It's been a tough week after the performance at Manchester City and the way we played for much of the cup tie against Macclesfield.
"It's difficult with fans having a go at you after only two games but West Ham fans are second to none when they get behind the team and that's what we want. I can take any flak."
Blackburn boss Paul Ince:
"Everything went against me today and everything went for Curbs. I'm not happy because we had enough chances to change the course of the game.
"Curbs is obviously a lucky manager but I know he's also a top manager and I'm pleased for him."
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