Jeev, who shot 69 in the third round ended in a tie for 38th, his best in what has so far been a rather disappointing season for India's number one golfer.
Jeev had three birdies and three bogeys in the final round after being two over after 10 holes.
Jeev birdied the 11th and 17th to ensure he did not fall too deep. The other two Indians, Shiv Kapur and Gaganjeet Bhullar had missed the half cut.
Ilonen started the day in lead and was two shots clear of Edoardo Molinari, who had set the clubhouse target at 12-under 272.
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Ilonen went into the trees but got to the green in four. He then needed a two-putt from 10 feet to win outright and he did exactly that despite finishing with a bogey.
Ilonen had just two birdies on second and fourth and then a string of pars till that bogey on 18th. The win would be a big boost for Ilonen, who has already qualified for British Open next month.