"I want to say first of all, congratulations Anett, you played really well today and I'm sorry," Sabalenka said before collecting the trophy. "I think we both showed our best tennis.
"Thank you everyone for your support. It's been an amazing week for me."
Sabalenka showed signs of early nerves and the first five points Kontaveit won all resulted from unforced errors by her opponent, but the Belarusian was clinical when it counted, converting her first break point chance to edge ahead.
She won 78 percent of her first serves and scorched the court from behind the baseline while showing a surprisingly deft touch at the net.
Kontaveit fought gamely in the face of the onslaught but had few answers to Sabalenka's power and guile.
The Estonian, who managed 10 clear winners and made half as many unforced errors, paid the price for landing just 45 percent of her first serves.
Up a break in the second set, Sabalenka moved in for the kill, claiming 16 of the final 20 points and sealing victory with her 25th winner of the match, a thunderous forehand down the line.
Victory means the Belarusian will rise four places to 16th in the world, above Serena Williams, when the new WTA rankings are released on Monday.
(Reporting by Simon Jennings in Bengaluru; editing by Clare Fallon)
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