The Romanian avenged this year's French Open final defeat by Ostapenko, which cost Halep the chance to top the rankings in June, with a ruthless all-round display in which she hit five aces and 14 winners to oust the Latvian in 75 minutes.
The 26-year-old takes over top spot from Spaniard Garbine Muguruza and will become the first Romanian to head the WTA rankings when the updated standings are released on Monday.
"It's very emotional, I think it's the first time I cried on court," Halep said. "It's amazing that I could do this. My team, everyone at home... is watching, and I want to thank everyone. It's my special day."
Ostapenko produced a lacklustre performance and recorded 32 unforced errors as she failed to make any inroads on her opponent's solid defence. Halep also broke the 20-year-old's serve four times, including in the first game of the match.
The Latvian showed some resistance in the second set to forge a 4-3 lead but Halep won three consecutive games to seal victory.
WTA CEO Steve Simon and tour president Micky Lawler presented Halep, who had come close to topping the rankings on three different occasions this year, with a memento to mark her achievement.
Wuhan Open champion Garcia raced to her 10th consecutive win to climb into the world's top 10 as an error-strewn Kvitova recorded 11 double faults and won just 10 of 27 second serves.
The 23-year-old took a 3-0 lead in the first set to pile the pressure on Kvitova, who failed to make a comeback and lost the set.
Twice Wimbledon champion Kvitova started the second set strongly to gain a 2-0 advantage but her wayward serving cost her as Garcia levelled at 5-5 before clinching the match.
Garcia is on course to win her second consecutive title but Halep has beaten her in both their previous meetings.
(Reporting by Aditi Prakash in Bengaluru; Editing by Ed Osmond)
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