Ben Duckett was the cornerstone of England's chase, scoring a triumphant 149 runs, supported by Zak Crawley's 65 in an opening stand of 188.
Joe Root contributed an unbeaten 53, and Jamie Smith finished with 44 not out, including two sixes, to seal the win with 14 overs remaining.
This chase marked England's second-highest successful pursuit ever and the 10th largest of all time in Test cricket.
India became the first team to lose a Test after scoring five individual centuries, with their collapse and dropped catches contributing to their defeat.