The 25-year-old Estonian captured the 30-minute first set with an ace out wide and sealed the win when Krejcikova sent a backhand into the net on match point.
Kontaveit, who was the final singles player to secure her place in the eight-player tournament, claimed four WTA titles this year to surge to world No 8 and has now won 11 straight matches.
"I managed to win Cleveland, then it just sort of started rolling from there," said Kontaveit, who also picked up titles in Ostrava, Moscow and Cluj-Napoca.
"I've been believing in myself a little bit more, and the game definitely has clicked from just getting more wins and playing a lot of tennis and really feeling comfortable, enjoying playing tennis."
The WTA Finals divides the players into two groups of four to play in a round-robin, with the top two players from each group advancing to the semifinals, where the tournament will then use a knockout format.
French Open champion Krejcikova, who is the only reigning Grand Slam champion in the competition, never found a rhythm on the purple court in the high-altitude Mexican city.
"The match was difficult," Krejcikova said.
"I think Anett, she was playing a solid game, she was serving well."
Former world No 1s Garbine Muguruza and Karolina Pliskova will play in the evening session.
The WTA Finals were not held last year due to the Covid-19 pandemic.