India completed just their seventh Test victory on English soil as they ran out 203-run winners on the final day at Trent Bridge.
Resuming on 311-9, James Anderson and Adil Rashid managed 2.5 overs before Ravi Ashwin took the final wicket, his first of the innings.
Anderson was the man to fall, caught at first slip off a spitting Ashwin leg-spinner for 11, as England were all out for 317, adding just six runs on the final morning.
The series now goes on to The Ageas Bowl, with the fourth Specsavers Test starting on Thursday 30 September, where England will once again be going for series victory.