Jadhav smashed 58 off 42 balls before Axar Patel (20 off 11) came up with a late cameo to take India to a competitive total.
India, batting first for the first time on the tour, had a tough time against the Zimbabwe bowlers on a pitch where scoring freely proved to be difficult, as it was the case earlier in the series.
It was a golden opportunity for the young batsmen to make an impact in a must-win match but some of them ended up squandering it.
Rahul was tentative at the start but bounced back in Chatara's following over, smashing him for a straight six and a couple of fours. Eventually, he did not last long and neither did his opening partner Mandeep Singh.
Mandeep, who scored 31 and 52 not out in the last two games, was the first one to go back. He tried to cut a short ball over cover but mistimed it to be caught just outside the circle.
With Manish Pandey run out after a brilliant direct hit from Elton Chigumbura, India were struggling at 29 for three in six overs.
Jadhav and Ambati Rayudu (20) were left to do the repair job and they took the innings forward with a 49-run stand off as many balls.
Barring Jadhav, the Indian batsmen could not find the big hits that were needed in the middle overs.
Captain M S Dhoni, who failed to get his team over the line in opening T20, was bowled by Donald Tiripano after making 9 off 14 balls.
Dhoni did not get going with the bat but added another feather to his illustrious cap when he walked out for the toss.
By playing this game, he equalled Ricky Ponting's record of captaining in 324 international matches to be at the top of the list alongside the Australian.
(REOPENS DEL 55)
The seamers did well to trouble the openers but failed to give any breakthrough as it was England's session, giving them a clear chance to reach 350-plus.
Put in, England were off to a watchful start with the ball moving around thanks to the green patches on the centre strip.
There was pace and bounce in the first over as Bhuveneshwar impressed once again hitting the deck and getting movements off the seam.
Drafted into the side in place of the injured Alex Hales, Billings had an anxious start and was lucky to survive with the ball beating his edge as both the openers remained on zero after two overs.
First it was a short ball and he guided straight to third man, but only for replays to show it was a no-ball by Bumrah.
Then with Pandya bowling, umpire Anil Chaudhary gave him a caught-behind dismissal before Bairstow went in for a successful review.
It's a short ball, cramping him for room, went in for a pull despite that and it seemed like he missed it but Dhoni loud appeal made it look like convincing.
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