Stephens stuns defending champion Garcia, Jabeur rallies in Cincinnati
Stephens was ecstatic after executing a perfect volley on match point to claim the win as the 2017 US Open champion looks to sharpen her game ahead of the year's final major, which kicks off later this month in New York.
"Thank you guys so much, it was so electric in here and so fun," Stephens said in an on-court interview under the lights.
"I felt like I played really well and was really consistent but honestly there is nothing better than playing in the U.S. in front of an American crowd. Incredible audience and atmosphere."
Stephens was tentative with her serve early on and was broken for a second time in the 10th game as Garcia grabbed the first set.
But the six-seeded Frenchwoman appeared rattled when she dropped her serve early in the second set and Stephens rode that advantage to level the match.
It looked like Stephens would run away with the decider when she raced out to a 3-0 double break lead but Garcia dug deep to level at 4-4.
But Stephens would not be denied, breaking back and coolly serving out the match to set up a meeting with either Wimbledon champion Marketa Vondrousova or Anastasia Potapova, who play their second-round match on Wednesday.
JABEUR FIGHTS ON
Fifth-ranked Jabeur, in her first match since suffering "the most painful loss" of her career in the Wimbledon final, clawed her way from a 1-5 deficit in the final set to beat Ukrainian Anhelina Kalinina 6-3 6-7(2) 7-6(2).
The victory highlighted Jabeur's mental toughness and she pointed to her head after sealing the win.
Kalinina, who suffered early exits in Montreal and Washington, showed fighting spirit as she broke Jabeur on the fourth try to set up the second-set tiebreak.
But a malfunctioning serve with six double faults in the final set undermined her best efforts and Jabeur was firing on all cylinders when they reached the tiebreak, where the Tunisian clinched it with a backhand winner.
"It's really nice to know where I can go, what I can push, you know, and today was really tough. It was tough to believe I could win this match," said Jabeur, who is into the third round after a first-round bye.
"A lot of frustration in that third set but I'm glad I kept going."
Twice champion Victoria Azarenka upset Czech 11th seed Barbora Krejcikova 6-3 7-5 to reach the second round.
The unseeded Belarusian Azarenka broke Krejcikova four times, saved three of five break points and won the final five games of a match lasting one hour 45 minutes.
Krejcikova battled to get the opener back on serve but Azarenka broke right back and then went on to serve out the first set in the following game on her second set point.
In the second set, Krejcikova grabbed the early momentum and it was Azarenka who had to come back from a break down and then kicked into a higher gear before saving two break points in the final game to serve out the match.
"I am just a fighter and I will keep going until I get it right," Azarenka said during her on-court interview.
"My mentality has been like this since I'm a kid. Growing up not in the greatest conditions I had to fight for everything and that really shaped my personality today."
WOZNIACKI EXITS
Danish wildcard Caroline Wozniacki, in her second tournament out of retirement, lost her opening match 6-4 6-4 to lucky loser Varvara Gracheva of France.
Wozniacki had her chances but failed to convert any of her nine break points and Gracheva's backhand proved too much for the former world number one to handle.
Wozniacki reached the second round last week in Montreal, where she played her first competitive matches after more than three years away to start a family.
Czech ninth seed Petra Kvitova, a Cincinnati finalist last year, also booked her spot in the second round with a 7-6(2) 6-0 win over Russian Anna Blinkova.
In other early action, Jelena Ostapenko beat former Cincinnati champion Karolina Pliskova 1-6 6-3 6-4 and will next face fourth seed Elena Rybakina.