The third-seeded Zverev won 4-6, 6-3, 6-2 against big-serving Gilles Muller, after the fourth-seeded Dimitrov had rallied to beat Pierre-Hugues Herbert 3-6, 6-2, 6-4 and the fifth-seeded Thiem saved a match point in his 5-7, 7-5, 7-5 win against Andrey Rublev of Russia.
Zverev won with the floodlights illuminating center court and the crowd fading along with the light. Muller saved the first match point with a strong serve but lost to the imposing German on the next with a double fault.
The 20-year-old Zverev had appeared in control of the first set when he broke for a 4-3 lead. But Muller broke straight back, held, and broke again with a neat drop shot to take the first set. Zverev took control of the second set after Muller dropped his opening serve and then broke him again to clinch it.
Zverev next plays with 13th-seeded Fabio Fognini or Jan-Lennard Struff in the third round.
Earlier, Dimitrov his serve twice in the first set against the 82nd-ranked Herbert. Serving at 5-3 and 15-40 down, he mistimed a forehand and the ball went off the racket frame and into the crowd.
But the Bulgarian found his range in the second set, securing consecutive breaks on the Frenchman's serve before serving it out at love.
Dimitrov broke Herbert in the fifth game of the decider, then immediately dropped serve with another wild forehand before breaking the Frenchman again for 4-3. He sealed the victory on his first match point when he whipped a powerful forehand to the back of the court, which Herbert returned long.
"I was just a little bit rusty, I haven't played a match for almost three weeks," Dimitrov said. "All I (could) do was just fight and win. How doesn't really matter."
It was even harder for Thiem.
He saved a match point when Rublev served at 5-4, 40-30 but hit a forehand narrowly wide.
Thiem made the most of the reprieve, breaking him with backhand pass down the line and holding for 6-5.
The Austrian was 15-40 up on Rublev's serve and also converted his first match point, when Rublev double-faulted with a weak serve into the net.
"I was 10 centimeters from being out of the tournament," a relieved Thiem said. "But I'm happy that I played two hours and 40 (minutes)."
Thiem has reached the French Open semifinals for the past two years. He next meets 12-time Grand Slam champion Novak Djokovic or Borna Coric of Croatia, who play their second-round match on Wednesday.
"I'm looking forward to watching Djokovic and Coric in front of the TV, and then playing the winner on Thursday," Thiem said.
No. 6 David Goffin of Belgium needed four match points to beat qualifier Stefanos Tsitsipas 7-6 (4), 7-5, while Zverev's older brother, Mischa Zverev also reached the third round by beating No. 7 Lucas Pouille 2-6, 6-1, 7-6 (3).
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