The lanky speedster, whose consistency has always been under the scanner, delivered when it mattered most, as he grabbed a career-best 7 for 74 to bowl out the home team for a 223 in pursuit of a competitive victory target of 319.
From a relatively comfortable 173 for four, the last six wickets fell for only 50 runs with the final five coming in only 12.2 overs after lunch on an absorbing fifth day's play.
It also marked Mahendra Singh Dhoni's first significant victory as Test captain outside the sub-continent. The last time India won a Test match outside the South Asian region was back in 2011 when they defeated West Indies in a 1-0 series win.
The victory was achieved in the 89th over when James Anderson tapped a Ravindra Jadeja delivery towards short cover and set off for non-existent single but Jadeja was alert enough to pick up and break the stumps down with a direct throw triggering off instant celebrations.
Resuming at a precarious 105 for four on the final day, the two overnight batsmen Joe Root (66) and Moeen Ali (39) batted with a lot of determination adding 101 runs in 44.4 overs before Ishant struck at the stroke of lunch.
He got one to rear up awkwardly as left-hander Ali took his eyes off the ball in order to fend it. The ball lobbed up at short leg for Cheteshwar Pujara to complete a simple catch.