The 23-year-old eked out a 21-11 17-21 21-13 win over Bae in a match that last for one hour at the Kuala Lumpur Badminton stadium.
World number six Saina had suffered back-to-back defeats at the hands of Minatsu Mitani of Japan and world number one Chinese shuttler Li Xuerui in her two matches of Group B singles competition, which had put her in a must-win situation today.
In today's match against world number seven Bae, Saina needed a straight-game victory to have a better chance of making the cut.
But now, even if Xuerui packs off Mitani in straight games later today and there is a three-way tie among Saina, Bae and Mitani for the second place in the group, according to the tournament rules it will be the difference of games won and games lost that will decide who among the trio will qualify for semifinals as Group B runner-up.
In the opening game, from 6-6, Saina registered six straight points to gather a healthy lead. The six point run was broken when Saina hit long but the Indian continued to dominate and reached 15-7. But a series of unforced errors saw Bae trim the lead to 10-15.
Saina then engaged her rival in an aggressive rally and finished it with a good net play. The left-handed Bae found it difficult to negotiate Saina's better net play and allowed the Indian to take a 18-10 lead.
A couple of points more and Saina was sitting comfortably on a 10 game points but the Indian rushed into a net shot as Bae saved one game point but the Hyderabadi didn't make any more mistake and nosed ahead when the Korean hit wide.
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