Joshi (71-76) was at three-over 147, while the other Indians surviving for the weekend were Rashid Khan (69-79) in tied 30th, Abhijit Chadha (67-82) in tied 40th, Chiragh Kumar (73-77) in tied 50th and Angad Cheema (78-73) in tied 58th.
Also making the cut was Daniel Chopra (73-76) in tied 40th place.
Gaganjeet Bhullar (75-77) and Rahil Gangjee (78-74) missed the cut by one shot as the cut fell at seven-over 151, and the others missing out were S Chikkarangappa (78-76), Himmat Rai (72-82) and Arjun Atwal (78-83).
Singapore-based Australian Unho Park battled the conditions before signing for a second round one-over-par 73 to stake his place atop the leaderboard.
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Park continued to put himself in contention for his maiden Asian Tour win at the USD 750,000 Asian Tour event at the Royal Jakarta Golf Club with his two-day total of four-under-par 140.
Joshi did well to par the entire back nine, which was his first nine, but then had one birdie, three bogeys and one double on the second nine in his 76.
Rashid Khan, twice winner on Asian Tour in 2014, had seven bogeys, two birdies and one bogey in his card.
Overnight co-leader Chan Shih-chang of Chinese Taipei eagled his closing ninth hole to haul himself back into contention, taking the outright second place with a 75 after struggling for most part of the day.
Thailand's Namchok Tantipokhakul and Chapchai Nirat signed for matching 142 total to share third place with Denmark's Thomas Bjorn and Japan's Yosuke Tsukada while birthday boy Lee Westwood of England returned with a 74 to stay in touch with the leaders in seventh place.