Jeev, who was four-under after 12 holes finished at one-under 71, and at 11-under 273.
Meanwhile the long nine-year wait for his maiden European Tour title ended for Robert Rock, who completed a start-to-finish victory with a closing 67 that left him 21 under for the week, one ahead of Thorbjorn Olesen and Gary Boyd. Rock was playing his 209th Tour event.
With the course set up in a way to offer a lot of birdie chances at the Royal Park I Roveri, the early target was set by the 21-year-old Dane Thorbjorn Olesen, who after a stunning front-nine 29 completed a 62. He finished just as long Rock started.
Jeev had a flawless front nine with two birdies on fourth and sixth. An eagle on par-5 11th saw him move to 15-under and there was distinct possibility of the Indian making a move for top-5.
But he hit a rough patch with bogeys on 13th, 14th, 16th and 17th before a birdie on 18th gave him small consolation. The other two Indians, Shiv Kapur (74-67) and SSP Chowrasia (73-73) earlier missed the halfway cut.
Rock, two clear overnight, bogeyed the third after failing to get up and down. Then he moved into an overdrive, reeling in four consecutive birdies from the fifth, and had further birdies on the tenth and 11th, which carried him ahead of Olesen.
He survived a bogey on 12th and made up by holing a 15-footer on 13th. He endured a couple of testy par putts and on 17th, he was in big trouble when his drive at the 17th went way right into the trees.
However, he produced a fantastic escape onto the fairway by hitting through the tree and even slightly clipped a branch. He pitched to 12 feet and bravely holed his clutch putt for par.
Scotland's Pete Whiteford claimed his third consecutive top-ten finish as he finished fourth on 19 under, one ahead of Dutchman Joost Luiten.
There were large galleries following the action once again in Turin, but local favourite Francesco Molinari and 18-year-old sensation Matteo Manassero struggled as they finished in a share of eighth place
