"Honestly I don't know (how I won)," Brengle said after reaching the quarter-finals with the biggest win of her career against an opponent 70 rungs higher than her in the WTA rankings.
"It's so cool. It's what you dream about, playing the best in the world.
"The last time I played her I only won one game, it got a lot better today," she said, referring to Serena's 6-0 6-1 win in their only previous meeting in 2015.
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The 26-year-old was 1-4 down before she staged a brilliant comeback to run away with the first set against the 22-times grand slam singles champion playing her first tournament since her semi-final loss at the U.S. Open last September.
Serena was a set and 4-3 down when she made a comeback of her own, breaking with a delicate drop shot and unleashing a running defensive forehand to clinch the tie-breaker and force the decider.
The third set went on serve until the 10th game when Brengle held two match points, only for Serena to fight off both and slump in relief when she hit a crosscourt forehand to get back to deuce.
Brengle strode confidently across court, secured her third match point and stared in disbelief as Serena double faulted to hand her the victory in two hours and 13 minutes.
On a day of disappointment for the family, Serena's sister Venus downed local favourite Jade Lewis 7-6(2) 6-2 but withdrew with a right arm injury.
"I love this tournament and I'm really sad that I have to withdraw, but I'm happy to have had the opportunity to be here again this year," Venus said in a statement ahead of her match against Japanese youngster Naomi Osaka.
(Reporting by Amlan Chakraborty in New Delhi and Greg Stutchbury in Wellington; editing by Sudipto Ganguly)
