Playing with a lot of passion and energy, the 253rd- ranked Ankita came out with relentless hitting to catch Lin by surprise and beat her higher-ranked rival 6-3 6-2 on the centre court at the R K Khanna Tennis stadium.
This was after 19-year-old Karman Kaur Thandi lost the first match 2-6 2-6 to world number 125 Yafan Wang.
The Indians were not sharp enough, lacked coordination and missed several chances.
India next play formidable Kazakhstan, who blanked Hong Kong 3-0, in a must-win tie tomorrow.
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It was Ankita's first win over Lin in fourth attempt as she lost twice to her on the Tour and once in the Fed Cup.
Lin pounced on the serve of the Indian initially and consistently hit on her backhand but Ankita was ready to return the compliment.
After playing four deuce points in the fourth game, Lin hit a slightly wide forehand to hand Ankita her first breakpoint, but the Chinese managed to save that.
Ankita found a stunning backhand service return winner to earn her second break chance but hit a forehand long.
Lin again made error with her forehand and this time Ankita did not miss out as she attacked the second serve of Lin to make an angled un-returnable backhand to break her opponent.
Lin did put some pressure on the Indian but Ankita kept the lead with her and closed out the set in her favour in the ninth game.
Ankita kept up the tempo and broke Lin in the first game of the second set when the Chinese faltered with her backhand at 30-40.
The Indian lost her serve for the first time in the match immediately after getting the break but did not allow the Chinese to disturb the momentum by breaking her again in the fifth.
She hit a forehand on first breakpoint but on the second, the Chinese hit a forehand wide as Ankita led 4-1. It was a matter of time for Ankita from there.
Earlier, in the first match, the gulf between the players was evident with Wang striking the ball with authority while Karman's game was littered with errors.
The Chinese team arrived only yesterday morning but Wang still managed to adjust to the bounce of the centre court and the conditions.
It was the second meeting between Karman and Wang, who now leads the head-to-head 2-0, having won the first match during the Tianjin ITF event last year.
Wang stamped her superiority from the beginning as she broke Karman in the very first game of the match.
Karman tried too hard and even changed the tactics by approaching the net but Wang was up to the task as the Chinese found easy passing winners and forcing the Indian to retreat.
Karman had two chances to break her opponent second game of opening set and sixth of second but she could not.
Karman's serve was good only in patches as she served five double faults. In the few rallies also it was the Chinese who handled the points well.
Karman's unending unforced errors never let her come back in the match and one such long backhand ended her struggle on the court.