After a mixed American tour, with a semi-final in Indian Wells and an early loss to David Goffin in Miami, the 21-year-old Spaniard made a successful return to clay.
His only previous appearance in Monte Carlo in 2022 ended in a three-set defeat by Sebastian Korda.
The 21-year-old Spaniard, ranked two in the world, made a slow start against the lively Argentine who outlasted him in extended cross-court rallies.
After gaining an early break, Alcaraz gave up four games in a row which was enough for Cerundolo to go on and take the set.
From then on, however, it was all Alcaraz. He dropped just a single game over the next two sets as he blasted his way to victory in one hour and 37 minutes.
"I didn't start well," said Alcaraz. "I made a lot of mistakes and I let him play inside the court, dominating the points.
"I just knew that I had to do something else, play more aggressively, and play my own tennis: drop shots, going to the net and show more aggression.
"The most important change was the return, I tried to return closer to the line and push him."
The world No.3 booked himself a last 16 date against the German Daniel Altmaier, 84th in the world, who saw off the French veteran Richard Gasquet 7-5, 5-7, 6-2.
Gasquet, 38, playing for the last time in Monte Carlo, was given a warm reception by the crowds who have been watching him since he made his tournament debut as a 15-year-old wildcard in 2002.
"I started with (Andre) Agassi and I'll finish with Alcaraz," said Gasquet who will retire from the circuit after the French Open."It's a gap of almost 40 years, it's enormous."