American sixth seed Coco Gauff told herself she "should not freak out" before fighting back to avoid a shock early exit at the French Open.
Gauff won 3-6 6-1 6-2 against Spain's Rebeka Masarova, while top seed Iga Swiatek won 6-4 6-0 against another Spaniard, Cristina Bucsa.
Seventh seed Ons Jabeur has struggled for court time because of injury but beat Lucia Bronzetti 6-4 6-1.
Wimbledon champion Elena Rybakina won 6-4 6-2 against Brenda Fruhvirtova.
Kazakhstan's Rybakina is seeded fourth after winning the Rome title, where she proved she could be a threat on clay as well as the other quicker surfaces.
But Poland's world number one Swiatek remains the favourite to win a third title at Roland Garros, despite suffering a thigh injury in the build-up.
Swiatek, who also won the US Open last year, took time to find her rhythm in her first match since retiring from her Rome quarter-final against Rybakina because of the problem.
But she remained patient, found her range and then clinically brushed aside Spanish world number 70 Bucsa, needing just 22 minutes to win the second set.
Asked whether she feels the pressure in Paris, Swiatek said: "Of course I feel pressure. I think we all feel pressure. I would be lying if I said I don't.
"But I'm trying to work with it and play my game no matter the circumstances and the expectations from the outside.
"It's not easy but I think it's the most important thing in tennis right now to cope with that properly, and I already know how to do that."
Gauff uses Heat as inspiration to win
Gauff was the Roland Garros runner-up last year, losing to Swiatek in her first major singles final, but found her progress at the first hurdle this year not straightforward against 71st-ranked Masarova.
However, she demonstrated a mental resilience which she said was inspired by the Miami Heat beating the Boston Celtics in the Eastern Conference Finals to reach the NBA finals.
Heat, who the 19-year-old Floridian supports, led 3-0 in the best-of-seven series, were pegged back to 3-3 but won the decider on Monday.
"I told myself if Jimmy Butler [Heat star] didn't freak out when up 3-0 and all of a sudden it was 3-3, then I shouldn't freak out when losing the first set," said Gauff, who did not watch the game because of the time-zone difference.
After not winning back-to-back matches on the European clay this season, Gauff endured a difficult opening set where she lacked trust in her shots and was unable to take any of eight break points.
But she began to grow in confidence from the start of the second set and the increased aggression of her shots forced Masarova into more errors.
Having not won from a set down in her previous 15 matches, Gauff teed up a meeting with Austrian world number 61 Julia Grabher in the second round.
"You have the choice to dwell on it or reset, and I chose to reset," she said.
Jabeur still trying to get back to 100%
Like Gauff, Wimbledon and US Open finalist Jabeur came into the tournament lacking form.
Before facing Bronzetti, she had played one match since retiring injured against Swiatek in Stuttgart on 22 April.
Last year Jabeur was beaten in the first round on the Roland Garros clay but avoided the same fate by making strong starts to both sets against 65th-ranked Bronzetti.
"Obviously I'm trying to get back to my level 100%, and I think that will come match by match and by playing more matches," she said.
"I'm happy that I'm healthy and I'm moving well on the court."
Jabeur, 28, faces France's world number 122 Oceane Dodin in the second round.
Elsewhere, 2021 champion Barbora Krejcikova suffered her second straight first-round exit at Roland Garros since winning her first major singles title at the event.
Krejcikova, 27, was beaten 6-2 6-4 by 34-year-old Ukrainian Lesia Tsurenko.
Meanwhile, Canada's Bianca Andreescu, 22, came back from a set down to defeat Belarusian 18th seed Victoria Azarenka 2-6 6-3 6-4.
The 2019 US Open champion, who tore two ligaments in her left ankle at the Miami Open in March, eventually clinched her fifth match point after two hours and 30 minutes on Court Simonne Mathieu.
Croatia's Petra Martic also produced a fightback to overcome American 32nd seed Shelby Rogers 3-6 6-3 6-2.
French 20-year-old Diane Parry defeated Ukrainian 25th seed Anhelina Kalinina 6-2 6-3, while Romanian 30th seed Sorana Cirstea fell 7-5 2-6 6-2 to Italy's Jasmine Paolini and Czech 31st seed Marie Bouzkova lost 6-4 7-6 (7-5) to China's Wang Xinyu.