World No. 7 Saina, seeded seventh in the tournament, lost the first game, but rallied in a fine fashion to prevail over her 13th seeded Japanese rival in a match that lasted an hour and five minutes at the Ballerup Super Arena here.
Saina will take on World No. 1 Li Xuerui of China in the last eight stage of the tournament.
The World No. 14 Japanese straight away opened up a 4-0 lead and throughout the game, Saina was lagging behind. The nearest she could reach her rival was at 5-6.
In the second game, the Indian got her act together and surged ahead with a 7-3 lead, but Takahashi soon earned four consecutive points to make it 7-7 and then moved swiftly to extend the gap.
But just when it was looking as if it was all over for Saina, she maintained her clam to brought the gap down to 15-16 before catching Takahashi at 17-17.
At 18-18, Saina upped the ante and reeled off three straight points to take the match to the decider.
The third and final game turned out to be a cake walk for India's ace shuttler, who broke away from a tied 7-7 situation to topple her rival 21-12 at the end.
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