Less than a week before the Australian Open -- the season's first Grand Slam -- the American was twice two points away from losing to 72nd-ranked Ekaterina Alexandrova, who had the former US Open champion on the ropes.
Alexandrova won the first set to love and was serving for the match and two points away from victory in the second set. But Stephens somehow rallied to win 0-6, 7-6 (7/3), 7-6 (7/3).
"I was, like, it's not going to get any worse than this," Stephens said of the first set.
"So it was like I might as well just play.
The Czech, who slumped to 29 in the world after being attacked in her home by a knife-wielding man in 2016, has battled back to number eight and was encouraged by her 6-1, 7-5 win over the Belarusian.
Sabalenka is a form player, racing to number 11 in the world after a stellar 2018 and starting the year by winning the Shenzhen Open.
"She was definitely (finishing strongly). She came from Shenzhen (last week) where she won the tournament so I knew it would be a tough match," said Kvitova.
"Unfortunately I lost (to her) at the US Open but I'm happy with my performance here in the first round."
Kvitova belted 28 winners to Sabalenka's 11 and won an incredible 85 percent of her first-serve points during the 79-minute contest.
She is aiming for her second Sydney title after lifting the trophy in 2015.
There was no such joy for 2017 French Open winner Jelena Ostapenko, whose poor form continued in a 6-3, 6-3 defeat to Australia's Ash Barty, who is rewarded with a second-round clash against world number one Simona Halep.
Last year Muguruza was the top seed and world No.2, but 12 months on she is unseeded and down to 18.
"It was especially tough because Carla and I, we are friends, and it's very difficult to play against each other," said the former Roland Garros and Wimbledon champion. In the men's draw Australian teenager Alex De Minaur, a finalist last year, continued his preparations for the Australian Open with a 6-4 6-3 win over Dusan Lajovic.
Towering Americans Sam Querrey and Reilly Opelka are also through to the next round.
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