The two-time grand slam semi-finalist dropped only five points on her serve in the decider to collect her first win of the tournament.
"Today was a survive-and-conquer kind of day. I really was playing not so well, very below average for the standard that I'm used to playing and competing at," Vandeweghe, the second seed, told reporters.
"I think it was just a matter of focusing on the next point at hand and just moving forward. It's a tough part of the year and it's a tough event."
Fourth seed Anastasia Pavlyuchenkova opened her campaign with a 6-3 3-6 6-2 win over former world number one Angelique Kerber of Germany in the Rose Group.
The 26-year-old Russian rallied back from an early break down in the final set to continue her impressive run in Asia, after a runner-up finish in Tokyo followed by her third title of the year in Hong Kong earlier this month.
Germany's Julia Georges held off a late charge from Magdalena Rybarikova of Slovakia to win 6-1 7-6(5) in the first match of the Azalea Group.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
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