Sandhu (72-69-66), who was lying tied eighth and eight shots off the lead after round two, brought home the day's best card to lie two strokes adrift off Mukesh at the Kalhaar Blues & Greens with a total of nine-under 207.
Earlier in the day, the second round, which was incomplete due to the rain, was completed by 9 am. Mukesh held a four-shot lead at 11-under-133 at the halfway stage. Udayan Mane occupied second at seven-under-137. The cut went at five-over-149 with 51 players making it to the money rounds.
The 52-year-old veteran's three birdies were accompanied by an equal number of bogeys as his putter went cold.
Mukesh, who has three top-5s this year including a win in Kochi, had a horrid time on the par-5 12th where he found the water with his second shot and as a result dropped a bogey.
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Sandhu, who like Mukesh, also has a win and two other top-5s to his credit this season, produced a strong front-nine with four straight birdies from the third to the sixth.
Sandhu, currently third on the PGTI Order of Merit, said, "The good start and finish was the key for me today. I began with some decent par-saves on the first two holes that helped me grow in confidence.
"Thereafter, the four birdies in a row got me back into the match. That's when I was expecting to shoot a really low number. But I lost some momentum in the middle stages. My focus on the last day will be to play my own game and not try to overpower the course," added Ajeetesh, who won on the PGTI earlier this year in Hyderabad.
Delhi's Honey Baisoya (71) and Anura Rohana (72) were a further shot back in tied fifth.
Delhi's Chiragh Kumar was tied 10th at two-under-214 while Shamim Khan (Order of Merit leader), another Delhi golfer, occupied tied 14th place at one-under-215.
Panchkula-based Shubhankar Sharma was tied 24th at three-over-219 while Bengaluru's Khalin Joshi was tied 33rd at five-over-221.