Tamim Iqbal scored 104 for the hosts who lost their last nine wickets for 49 runs after skipper Mushfiqur Rahim won the toss and opted to bat.
Off-spinner Moeen Ali took five for 57 while paceman Chris Woakes took three wickets for England, who lead the series 1-0.
(Reporting by Sudipto Ganguly in Mumbai; editing by Nick Mulvenney)
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