Jeev, who started the day way back in tied 16th spot, registered a bogey-free five-under 67 and moved into clubhouse lead. Then he waited for nine more groups to finish and found himself in a play-off with Francesco Molinari.
"This is an amazing win. I waited for more than an hour, maybe longer to see if I was getting into a play-off. (Marc) Warren was playing well and then Molinari, too. I felt I had an outside chance of being in a play-off and after I finished lunch, there it was all of a sudden. I am glad I could pull it off," said Jeev soon after the win.
"I knew I was playing well," he said earlier after his regulation play.
"I have been having good rounds but not good tournaments. To have a good tournament you need to put together four good rounds and this week I did that," said Jeev.
The win was Jeev's fourth in an European Tour event. His earlier wins were Volvo China in 2006, Volvo Masters of Europe in 2006 and the Austrian Open in 2008.
In the first play-off hole, Jeev birdied from 15 feet, while the Italian missed from 25 feet to give the Indian his first win since 2008 and with it a berth in the Open.
On a tough day for scoring, Jeev had a stunning start with four birdies in first six holes. He became five-under on 10th, but then had eight pars in a row, including a birdie miss on 18th.
A little earlier, another Indian golfer SSP Chowrasia carded 72 in the final round to finish tied 11th, his best finish since the 2010 win at the Avantha Masters.