Strike partener Eidur Gudjohnsen also got a brace and Mikael Forssel the other, with Jermain Defoe scoring a consolation for the visitors.
And Hasselbaink said of his goalscoring record against Chelsea's London rivals: "I didn't realise. I don't think about these kind of things - honestly.
"It was important to get three points - and we all did that together, working very hard."
He continued on Sky Sports: "It was very important to score the first goal - I think that almost gave West Ham a KO.
"I think in the second half we put in a good performance."
The striker has been struggling with an upper thigh injury in the last few days and admitted: "I was a little bit tired at the end - but I felt almost 100 per cent fit and I was up for it today."
"Players like (Paolo) di Canio, (Michael) Carrick and (Joe) Cole have a lot of quality - but (Gianfranco) Zola, (Eidur) Gudjohnsen and Jimmy Hasselbaink have a lot of quality too."
Chelsea's Italian boss believes victory was vital to keep his team's outside hopes of the title alive.
He added: "It was important to stay near the big group because if we had lost or drawn today the group was very far. But now it's important to stay very, very near them."
West Ham goalkeeper David James agreed that Hasselbaink's opening goal just before half-time was the game's turning point.
The Hammers keeper said: "Any time is bad to concede - but the manner was the worse thing. No-one was picking players up.
"They had a very powerful front line but the manner in which we approached the second half wasn't the best - which is disappointing considering how we've played of late.
"We gave away a few silly balls which I think were costly in the end."
James said that the dismissal of Paolo di Canio made West Ham's plight more difficult.
He added: "Ultimately we were under pressure with 11 men - and things don't become any easier with 10.
"It's the first time I've let five goals in in my career - but it could have been more today."
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