The German No.3 seed survived a late fightback from the world No.36 and bellowed his relief when Baez sent a forehand wide on match point.
Zverev, 25, won in five sets, 2-6 4-6 6-1 6-2 7-5, but said he "couldn't have played worse at the beginning" on Wednesday.
It was the fifth year in a row that Zverev, who achieved his best result at Roland Garros when he reached the semi-finals last year, had to go through a five-setter in one of the opening two rounds.
"I lost a US Open final being two sets up and I've learned from it. He's unbelievable and he's got a bright future ahead of him," Zverev said of his opponent, who won his maiden ATP title in Estoril this month.
"I just tried to fight. You have to win these kind of matches, when you're not playing well because you can't always play well."
Zverev looked out of sorts in the opening set, allowing his opponent to race to a 5-1 lead practically unchallenged on a windswept court Philippe Chatrier.
He trailed 4-0 down in the second before starting to find his range and while it was not enough to save the set, the German carried the momentum into the third.
Clicking into top gear, Zverev went 3-0 up and won five games in a row to open a 2-0 lead in the fourth set, which he won comfortably.
The 21-year-old Baez looked completely overwhelmed, but then fought tooth and nail to break for 4-2 in the decider as Zverev's unforced errors crept up again.
The German broke straight back with a backhand winner down the line but faced a match point at 5-4, which he saved with a big first serve.
Zverev then broke for 6-5 as Baez fired a backhand wide and he played a solid last game to set up a third-round encounter with American Brandon Nakashima.
World number one Novak Djokovic's 6-2 6-3 7-6 (7-4) victory over Slovakia's Alex Molcan was far more straightforward.
On a blustery Court Suzanne Lenglen, the 35-year-old Djokovic cruised through the opening two sets, breaking Molcan's serve three times without giving the Slovakian a single opportunity on his own.
The 24-year-old Molcan, trained by Djokovic's former long-time coach Marian Vajda, opened up his shoulders in the third set and forced a tiebreaker.
But Djokovic moved up a gear and converted his second match point when the left-hander found the net with a return.
He will next meet Slovenia's former world No.43 Aljaz Bedene for a place in the fourth round.
With agencies
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