The Liberal Democrats more than doubled their vote from 3,264 in 2001 to 8,608.
Muslims make up around 25% of Blackburn's 100,000-strong population and there was speculation Mr Straw would suffer from an anti-Iraq war backlash.
Mr Straw said: "Many predictions were made about the result in Blackburn. I can't remember an occasion when Blackburn has had quite so much press attention, with predictions that the Labour party might even lose.
"We didn't lose. We had a terrific victory and the fact of the victory is down to the strength of the Blackburn Labour party.
"In this multiracial, multi-ethnic town, it is the strongest of all organisations in bringing faiths and communities together."
Liberal Democrat candidate Tony Melia said: "It was a mountain for us to climb and I think we have had a remarkable result.
"It shows people are interested in our policies and next time we will be better and back."
Turnout at the Blackburn poll was 57.94%, compared with the 2001 figure of 55.5%.
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