After setting their hosts a target of 299, England took to the field and started off positively in the opening overs, until Patel and Rahane got into their stride and managed to reach 50 without loss with some impressive boundaries.
India's duo continued to progress, racking up 73 runs until England finally got the breakthrough when Tim Bresnan got Patel out for an lbw.
Despite claiming their first wicket, England failed to capitalise on any momentum and the partnership of Rahane and Gambhir scored 127 runs in 24 overs.
As the home side edged nearer to the 200 mark, Pietersen caught out Gambhir from a Steven Finn throw, keeping England in the contest.
A third and fourth wicket were taken in quick succession after Rahane and Raina were caught out by Cook and Pietersen.
England continued to build on the pressure after Graeme Swann claimed his first wicket of the day by taking out Kohli.
The last remaining overs were tense and frantic for both sides as India needed 17 runs to win from 12 balls with Jadeja and Dhoni in impressive form.
Despite countless opportunities England failed to stop India from triumphing and the home side finished off the third ODI on 300-5 to claim the series.