The 20-year-old Joshi, making his professional debut on the Asian Tour, chipped in for an eagle on 14 en route to a three-under-par 69 while Chan brilliantly birdied his last four holes for a 68 and a nine-under-par 135 total in the USD 300,000 Asian Tour event.
A shot back are India's Rashid Khan, who stormed into contention with a sensational 64, and Bangladesh's Siddikur, who returned a second successive 68. Another Indian Rahil Gangjee shot a 66 with two eagles to end the day two shots back.
Joshi, India's number one amateur last year, continued to shine against a strong field at the challenging Delhi Golf Club.
After turning in level par, he produced the shot of the round with an exquisite chip-in eagle on 14 before rolling in a six-footer at the last hole which he celebrated with a clenched fist.
"It's great. I hit the ball good although my putting wasn't great. I felt normal. I didn't feel any pressure. I just wanted to go out there and do the best that I could. I'm looking forward to the next two days. If the putter is hot, I know I'll do something," said Joshi.