The German fifth seed, who fought his way through a five-set thriller in the opening round, threw away a two-set lead against the 30th seed on Court Simonne Mathieu before setting up a meeting with Fabio Fognini.
It was a highly inconsistent performance by the lanky 22-year-old Zverev, who will need to sharpen his focus against the Italian ninth seed.
Monte Carlo Masters winner Fognini progressed with a 7-6(5) 6-4 4-6 6-1 victory against Spanish 18th seed Roberto Bautista Agut.
"He's been one of the best claycourt players this season, winning his first Masters, so obviously playing great tennis," Zverev, whose best Grand Slam came last year when he reached the last eight at Roland Garros, told reporters.
"Beating Rafa there, as well, and I think along the way a lot of good players - so it's going to be a difficult match.
"I think he's playing very well. Hasn't lost more than a set so far in a match. So it's going to be a difficult match."
Zverev did not make things easy for himself as he fell 3-1 behind in the opening set before managing to turn things around and take the lead.
He raced through the second only to find himself on the back foot again in the third and fourth as Lajovic forced a decider with temperatures flirting with 30 degrees Celsius -- in contrast to the chilly weather in the first week of the tournament.
After an early trade of breaks in the fifth, Zverev finally got his confidence back and finished it off with a whipping forehand, his 52nd winner barely making up for a woeful 55 unforced errors.
It was Zverev's fifth five-setter at Roland Garros, and he has won them all.
"It's a good thing to have in the back of your head. Hopefully I can continue this run. We'll see how it goes," the German said. "They didn't explain me the rules of five sets yet, so somebody needs to tell me I don't necessarily need to play five sets every time I step on the court!"
(Reporting by Julien Pretot; Editing by Hugh Lawson and Tony Lawrence)
