Chasing 247 on a Lord's wicket that had eased up after the first innings, India never found their stride and folded for 146 in 38.5 overs.
Topley (6-24) landed a double blow early in the chase by getting rid of opposition captain Rohit Sharma (35) for a duck and Shikhar Dhawan (36) for nine before Virat Kohli (33), returning from a groin strain, edged behind off David Willey (32) after a fluent start for 16.
"Terrific team performance to bounce back from the other day," said Topley, who was named player of the match.
"Happy to play my part. Means a lot, makes it all worthwhile.
"Had surgery like three years ago over the back of that stand, so it's come full circle.
"It's everyone's dream to play for England. Play my part to win games. Big game at the weekend."
Suryakumar Yadav (31) and Hardik Pandya (28) flickered briefly but failed to kick on after promising starts, falling for 27 and 29 respectively.
All hopes of an unlikely India win evaporated when Ravindra Jadeja (33) was removed by Liam Livingstone (28) for 29 as England sealed an easy win, three years to the day after they beat New Zealand in a dramatic finish to lift the 50-over World Cup at the venue.
Earlier, Yuzvendra Chahal (31) ripped through England's middle-order, claiming the prized scalps of Jonny Bairstow (32), Joe Root (31) and Ben Stokes (31), picking up figures of 4-47, as the home side were bowled out for 246 inside 50 overs.
England were put in to bat and Jason Roy (31) was the first to depart, chipping a Pandya delivery to fine leg after a scratchy 23, while Bairstow continued his rich vein of form before being cleaned up by Chahal for a breezy 38.
England's attempt to rebuild came unstuck after Chahal trapped Root (11) and Stokes (21) lbw before skipper Jos Buttler (31) missed a straight ball off Mohammed Shami (31) to be dismissed for four.
Livingstone took the attack to Pandya but the bowler got his revenge when the Lancastrian holed out in the deep after an entertaining run-a-ball 33. It took a late rally from Moeen Ali (35) and Willey to push England close to 250.
The teams now head to Manchester for the final game of the series on Sunday.
