The 21-year-old Shubhankar dropped five shots, including a double bogey at the 17th hole. But he responded with five birdies to get to the top of the leaderboard on seven-under par 209 at the DLF Golf and Country Club.
Wallace carded a 70 to share first place with Shubhankar. The Englishman scored an eagle and four birdies against four bogeys. The pair will go into Sunday with a one-shot lead over Stephen Gallacher of Scotland, who is in lone third place after carding a 67.
Argentine Emiliano Grillo, who had an overnight four-stroke lead at the top over Shubhankar, had a day to forget as he signed for a six-over 78. He is in tied fourth with Austria's Matthias Schwab (68) and England's Andrew Johnston (73) on five-under 211 total.
Sihwan Kim of the United States adopted an aggressive, yet calculated approach to card a 72. He is in tied-seven and just three shots behind the leaders along with Spain's Pablo Larrazabal.
Shubhankar is now in line to become the 10th Indian to win his National Open. If he wins, it would be the fourth time in a row that an Indian would have won the Indian Open following the success of Anirban Lahiri in 2015 and SSP Chawrasia in 2016 and 2017.
Shubhankar, who has scores of 73 and 64 in the first two rounds, said: "It was very windy today. The first two days were surprisingly calm. The course played really tough and I'm very happy with a 72. It was a mixed bag as everything happened.
"I holed out at the second, made a few good birdies and got a bad bounce on the 17th. I'm very pleased with the birdie at the last, which allowed me to grab a share of the lead. I'm looking forward to tomorrow.
"I'm just looking forward to playing out there again. I just want to have fun. It's the second week in the row I'm in the leading group. I'm going to draw from my experiences last week. I know it's going to be a battle out there tomorrow and I'll be ready for it."
Ajeetesh Sandhu (74) was the second best Indian as he occupied tied 26th spot with a 54-hole total of two-over 218.
Jyoti Randhawa (76) and Anirban Lahiri (75) were both in tied 32nd at four-over 220 three-round total.
Khalin Joshi was tied 37th at five-over 221, amateur Kshitij Naveed Kaul and Karandeep Kochhar were both in tied 48th at seven-over 223 while Udayan Mane was placed tied 56th at 10-over 226.
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