Root’s well-judged 113 from 108 balls on his home ground, his highest ODI score, lifted England to 294 for seven off their 50 overs.
Captain Alastair Cook chipped in with 46 and Jos Buttler fell for a breezy 49 after being run out by Mahendra Singh Dhoni.
Ravindra Jadeja played well to score a valiant 87 as India stuttered and stumbled during their run chase and were eventually all out for 253 with eight balls remaining.
“Joe Root played fantastically well. He went on and a couple of other guys supported him. That’s what we’ve been trying to do. We’ve got a lot of 20s and 30s in this series and when one of our guys went on and scored a century, we showed we’ve got a bowling attack to defend it,” Cook said at the presentation ceremony.
Man-of-the-match Root, who smashed 10 fours and three sixes, put on 108 runs with Buttler before Dhoni knocked off the bails to break the fifth-wicket partnership after Buttler set off for a non-existent run.
Mohammed Shami ended Root’s entertaining innings in the 46th over when the right-hander flicked the ball straight to Ravichandran Ashwin.
India’s hopes of completing a 4-0 rout got off to a rocky start when they lost Edgbaston centurion Ajinkya Rahane for a duck after he nonchalantly sliced a James Anderson delivery into the hands of Eoin Morgan in the first over.
From then on the visitors struggled to build momentum and they lost wickets at regular intervals, leaving all-rounder Jadeja frustrated as his swashbuckling knock of 87 off 68 balls turned out to be in vain.
The left-hander was last man out, clean bowled by Steven Finn in the penultimate over as he tried to score runs quickly in a bid to reach three figures in an international for the first time.
“We gave away too many wickets. There were quite a few soft dismissals and we were not able to score the number of runs we were supposed to. We are capable of getting 90-100 in the last 10 overs, but soft dismissals let us down,” Dhoni said.
Despite the defeat, India will be buoyed by their 50-overs performances in England as they look to fine-tune their game before beginning the defence of their World Cup title in February.
England, however, face an uphill task if they are to get their hands on the 50-overs World Cup, a trophy they have never won.
They have won only one series against another test-playing nation since 2012 and have lost their last four at home.
Their consolation victory has done little to paper over the cracks that run deep in England’s approach to the limited-overs format which some former players have labelled as old-fashioned and out of date.
“We know what we can do and it’s been really frustrating for the last few games that we’ve not been able to do it. One good game in four isn’t good enough,” Cook, who many pundits believe should step down as ODI captain because he is ill-equipped to prosper as a batsman in the limited-overs game, told the BBC.
“We now have a massive chunk of one-day cricket where we can concentrate on improving as players. The last time we had a focus like this we got to the Champions Trophy final (in 2013). The World Cup preparation will be perfect and hopefully we can all improve.”
(Writing by Pritha Sarkar in London, editing by Ed Osmond)