The golfer from Mhow was ahead by one at the Royal Calcutta Golf Club (RCGC) as his total read seven-under-137.
Delhi's Shamim Khan also fired a second round score of 68 to occupy second place at six-under-138. His was the only bogey-free round of the day.
Pre-tournament favourite SSP Chawrasia of Kolkata brought in a card of 70 to end the day in tied fourth at three-under-141.
The cut fell at five-over-149 and 54 professionals made the cut.
Mukesh (69-68) moved up two spots from overnight tied third to first as a result of his determined second round effort, which saw him fire five birdies at the expense of just one bogey.
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Mukesh's birdie on the eighth was negated by a bogey on the 10th but the oldest winner on the Asian Tour came roaring back with a trail of birdies on the 14th, 15th and 16th. He was in troubled waters on the 15th and 16th but made excellent recoveries to extract birdies on both holes.
"I have two victories at the RCGC, but it's been a while since I last won here, definitely over a decade. So I'm eager to perform well this time. I was quite pleased with the way I recovered on a couple of holes today. I was in the bunker on the 15th and in the rough on the 16th, but managed birdies on both occasions," Mukesh said.
Shamim (70-68) climbed from overnight tied seventh to second place after delivering the only bogey-free round of the day. Shamim sank three birdies from a range of 12 to 30 feet.
While overnight joint leader Chikkarangappa of Bengaluru slipped to third at five-under-139 after shooting a 71 on day two, local favourite Chawrasia made major gains with a 70 that took him from overnight tied 18th to tied fourth at three-under-141.
Chandigarh's Sujjan Song (71) and Sri Lankan N Thangaraja (71) joined Chawrasia in tied fourth.
Delhi's Rashid Khan and PGTI Order of Merit leader Ajeetesh Sandhu of Chandigarh were in tied 31st place at three-over-147.
Kolkata-based rookie Viraj Madappa (eight-over-152) missed the cut.