Playing in her third Olympics, the 31-year-old from Manipur, who finished 24th in the ranking round, dished out a dominating show to get the better off Lin 6-2, in the 1/16 elimination here.
Earlier in the 1/32 elimination round, the Indian had rallied her way to beat Austria's Laurence Baldauff 6-2.
Bombayla, who had lost in the second round of women's individual recurve event at the London Olympics, outclassed Lin 27-24, 27-24, 26-27, 28-26 to reach the pre-quarterfinals.
The Indian scored 8, 9, 10 against Lin's hat-trick of 8s to clinch the second set. In the third set, the Chinese Taipei girl hit the bull's eye twice even as Bombayla came up with a 7 and 9 in the first two shots. In the final shot, the Indian hit a 10 but that was not enough to win the set.
Earlier, Bombayla showed tremendous nerves as she bounced back after losing the first set to outclass Laurence in the second, third and fourth set in the first round.
Bombayla, who was the best Indian performer in the women's team event, scored a 24-27, 28-24, 27-23, 26-24 win in the 1/32 elimination round.
The 41-year-old Laurence started off well with a hat-trick of 9s in the first set to get the better of the Indian, who started off with a 9 but then shot 7 consecutively.
India's Atanu Das had also entered the pre-quarterfinals of the Individual men's recurve event yesterday.
