Baisoya's two-day total stood at seven-under-137.
Noida's Amardip Sinh Malik returned a 67 to climb into joint second along with first round leader C Muniyappa (72) of Bengaluru at five-under-139.
The cut was declared at five-over-149. Fifty-four professionals made the money rounds.
Baisoya's (72-65) error-free effort today pushed him up from overnight tied 15th to sole leader. The 19-year-old, still recovering from a wrist injury and suffering from fever since the last two days, surprised himself on day two, as he landed five shots within five feet.
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The teenager, ranked 21st on the PGTI last year, set up short birdie putts for himself on four occasions on the back-nine, all of which he converted. He also had a notable par-save after recovering from the trees on the 15th.
"If I can play like this while still down with fever, it certainly gives me the belief to do even better over the last two rounds. My iron-hitting was good and I kept landing it close," Basoya said.
Amardip Sinh (72-67) kept the local hopes alive with a 67 that featured an eagle and three birdies. His lone eagle and three birdie conversions, all came from a distance of four feet.
While he didn't concede any shots, he missed out on three birdie opportunities from five feet.
Muniyappa (67-72) conceded his overnight lead and slipped to joint second after a 72 on day two. Muniyappa struggled with his driving in round two and therefore mixed four bogeys and a double bogey with an eagle and four birdies.
Bengaluru lad Chikkarangappa (70) was placed tied 23rd at two-over-146.