England's victory, achieved despite Sachin Tendulkar's fifty, gave them a 2-0 lead in this four-match series as they looked to knock India off top spot in the ICC's Test Championship table.
Andrew Strauss's side will replace India at the summit if they maintain or better their lead in the remaining two Tests.
India set a record victory target of 478, were bowled out for 158 with Tendulkar top-scoring with 56 but still left searching for an unprecedented and elusive 100th international hundred.
Bresnan, who earlier made 90 batting at number eight in England's second innings 544, did the bulk of the damage with a maiden Test five wicket haul of five wickets for 48 runs in 12 overs -- including two in two balls before tea.
Only three India batsmen made double figure scores on Monday's fourth day, with Tendulkar the lone member of their powerful top order to achieve the feat.
No team has made more in the fourth innings to win a Test than the 418 for seven posted by the West Indies against Australia at St John's, Antigua, in 2002/03.
Before lunch England, who won the first Test at Lord's by 196 runs, saw off Rahul Dravid, who made 117 in India's first innings, for just six when he was caught behind off a lifting delivery from man of the match Stuart Broad.
Venkatsai Laxman, another of India's star batsmen, was then clean bowled by a superb James Anderson delivery for four.
Opener Abhinav Mukund, dropped on nought, struggled to three off 41 balls before falling to Bresnan's fifth ball, a bouncer he gloved to first slip Strauss.
And Bresnan succeeded with the short ball again when Suresh Raina hit a hook straight to substitute Scott Elstone at long leg.
Tendulkar had struck some typically sublime straight drives off Anderson but he could do nothing as Bresnan, only playing in this match after fast bowler Chris Tremlett was injured, took two wickets in two balls.
First Yuvraj Singh gloved a rising delivery to Alastair Cook at backward silly point and was out for eight.
Next ball India captain Mahendra Singh Dhoni, inexplicably playing no shot, was lbw for a golden duck to leave the tourists 55 for six and Bresnan on a hat-trick at the start of his next over, which Harbhajan Singh survived.
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