Jeev, trailing four-down at one stage, rallied to win 1-up on the 18th against Scott Hend, but Shiv Kapur allowed local man Richie Ramsay to make a comeback from three-down to win 1-up in another match.
Jeev, who has vast experience at Matchplay, started very slowly.
Hend, a seasoned campaigner, won the first two holes and then the fourth to go three up. He had birdied one each of them. He also won the sixth and seemed to be running away when Jeev bogeyed the par-4, just as he had done on fourth.
On the back nine, Jeev was a different player. He won five of the next holes, three of them with three birdies. Hend bogeyed 14th and 15th, as Jeev parred.
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Hend fought once more with a par par-3 16th to make it all square. But Jeev won the next hole with a par as Hend bogeyed and as both players parred the 18th.
Jeev has moved into the next round, where he will meet Julien Quesne, who beat Tom Lewis by the same margin of 1-up.
Ramsay, who interestingly won his first European Tour title with a win in play-off over Kapur in December 2009 at the South African Open, fought back, winning the eighth with a birdie and restored parity winning the 11th and 14th.
Ramsay went ahead for the first time with a birdie on par-4 17th. He holed a testy birdie on 18th as Kapur also birdied, but the Scot held onto his lead and moved into next round.