Down 0-2, the Indians showed great fighting spirit as the doubles pair of Dhruv Kapila and Chirag Shetty and PV Sindhu levelled the scores after reverses in the first two matches.
Sourabh will next face Korea's Heo Kwang Hee for a place in the men's singles final.
Seventh seed Sindhu lost 14-21 18-21 to Bing Jiao in the women's singles.
Sindhu leads India to 3-2 win over Hong Kong in Asia badminton Team Championship
Saina and Busanan engaged in some long rallies but it was the Thai shuttler who had the last laugh
In other matches, former Singapore Open champion B Sai Praneeth's fight lasted just 35 minutes as he went down 12-21, 17-21 to 24-year-old Ng Ka Long Angus in the second round. It was his third loss to the World No 15 from Hong Kong.
Following is the schedule of Indian contingent on the fifth day of the Asian Games.
PV Sindhu had to dig deep to down a fighting Vu Thi Trang of Vietnam but Saina Nehwal did not break any sweat as India's top two shuttlers advanced to the women's singles second round at the 18th Asian Games, in Jakarta, on Thursday.
A summary of sports events and persons who made news on Thursday.
Summary of sports events and persons who made news on Sunday
A summary of sports events and persons who made news on Saturday
Top seed Sameer, who won the Swiss Open earlier this year, had to dig deep into his reservoir to outwit compatriot Pratul Joshi 16-21, 26-24, 21-7 in 55 minutes. In another quarter-final, Gurusaidutt, a former Commonwealth Games bronze medallist, recovered from a game down to beat Malaysia's Lim Chi Wing 13-21, 22-20, 21-11 in 59 minutes.
