However, his fellow Indians - Shiv Kapur (74-67) and SSP Chowrasia (73-73) - missed the cut.
Jeev, who arrived late (on Wednesday evening) for the tournament as his son had fallen ill, played without a practice round.
He is now nine-under through two rounds in a tournament, which he says is going to be a low-scoring one.
“I have played blind in event before without a practice round and I have good memories of doing that at the Austrian Open, which I won (in 2008),” said the Indian ace.
“It is a good golf course and the scores are going to be low, so it is nice to shoot a good card,” he added.
Jeev is three behind the leader Robert Rock, who is at 12-under but has never won on the European Tour.
Rock (68) is one clear of first round joint-leader Chris Wood (69) and Dutchman Joost Luiten (67) at the Royal Park I Roveri. Like Rock, Wood is also looking for a maiden European Tour victory.
Jeev opened sedately and then birdied fifth and seventh and then added four more. He birdied the 10th and three in a row from 13th to 15th, at which point he was six-under.
He dropped a shot on 16th, but picked a birdie on 17th and closed with a par.
No fewer than six players are tied for fourth on ten under - including home trio Matteo Manassero, Francesco Molinari and Lorenzo Gagli.
Playing in his home city of Turin, Ryder Cup star Molinari carded a second round 68, and was joined not only by his compatriots but also in-form Frenchman Gregory Bourdy, Welshman Rhys Davies and England’s Gary Boyd.
Things were, however, not too good for the other two Indians - Kapur and Chowrasia.
Kapur had a superb second round, but even that 67 could not keep him for the weekend as the cut came at two-under 142 and Kapur was 143.