Spain’s Alcaraz looked subdued at times in a 6-3 6-4 2-6 6-2 victory over a player ranked 173 places below him.
Dutchman De Jong played well above his ranking but it was a rusty performance from Alcaraz, who had to twice come back from a break down in the fourth set.
“I prefer not to spend too much time on the court, I want to be in good shape for the next round but every match is different,” Alcaraz said.
“I was in trouble at points. Jesper and I put on a good show.”
Alcaraz will face either American Sebastian Korda or Kwon Soon-woo of South Korea next.
Stefanos Tsitsipas, the 2022 runner-up, and Andrey Rublev won their matches but no play was possible on the outside courts because of persistent rain.
In the night session, second seed Jannik Sinner dispatched Richard Gasquet in straight sets on Court Phillipe Chatrier – one of two courts at Roland Garros to have a roof.
On the other, Court Suzanne Lenglen, Switzerland’s 2015 French Open champion Stan Wawrinka lost in four sets to Russian Pavel Kotov.
This was almost the exact opposite of third seed Alcaraz’s dominant first-round win against lucky loser JJ Wolf.
The 21-year-old still had a compression sleeve on his right forearm – an injury which impacted his preparations for Roland Garros – and his lack of match practice showed.
After a relatively straightforward first two sets, it was as though Alcaraz’s concentration began to drift, often following a good shot with one that sailed wide or found the net.
He made 47 unforced errors, most of which came in the third set as he quickly went a double break down.
It looked as though the match could get even trickier for Alcaraz as he was immediately broken at the start of the fourth set, once again on a long forehand.
