It was just India's second Test match win at the Oval, coming 50 years after a four-wicket triumph at the south London ground gave them a first such success on English soil
The England captain will lead his side in the first of a two-match series against New Zealand at Lord's on Wednesday, with five more Tests against India before the English season is finished.
Off-spinner Dom Bess looks likely to earn a recall after two games on the sidelines. The 23-year-old was initially dropped for Moeen Ali, only to be overlooked again when he flew back home.
Skipper Joe Root gave Anderson the ball in the 14th over and he bowled Gill with an in-coming delivery to send the off stump flying. Three balls later he cleaned up Ajinkya Rahane for nought.
Leach took a single off Perera and number 11 James Anderson hit a boundary off Embuldeniya, who returned career-best figures of 7-137 in just his ninth Test, to add five runs to the overnight score.