Jeev, who has been struggling with his form of late, has now shot three straight rounds in 60s with 68, 69 and 68 to be 11-under.
Shiv Kapur (70) moved to nine-under and SSP Chawrasia had a very eventful finish with one birdie, one eagle and two bogeys in his final five holes.
Jeev had a bogey on fifth, but thereafter he was flawless with birdies on seventh and ninth and added another birdie on 12th before finding an eagle on 14th. He moved up to tied 16th after being 25th overnight.
At the top, Martin Kaymer fired a brilliant 65 to move into a share of the lead ahead of the final round.
The German was one of the favourites coming into the week as he looked for a first win since claiming his second Major Championship victory at the US Open at Pinehurst last year. But he will face a big challenge from joint-leaders Jens Fahrbring and Romain Wattel and the chasing pack.
