Second seed Nadal, gunning to become the first man to win seven Roland Garros titles, trailed Monaco 2-1 in the first set before winning the remaining 17 games to stay undefeated on Court Suzanne Lenglen since his French Open debut in 2005.
Monaco came out with all guns blazing but Nadal quickly doused his fire, with the Spaniard ending his opponent's ordeal after one hour and 46 minutes on his first match point.
Nadal, who has dropped only 19 games in four matches, next faces compatriot Nicolas Almagro, the 12th seed, for a place in the semi-finals.
The defending champion was gracious in victory.
"In my opinion, he was unlucky, unlucky in the first set. That's my feeling," he said.
"6‑2 was too much. Later, sure, very happy the way I played. I feel very, very sorry for him.
"I think he's playing probably the best tennis of his career, but probably not today after, especially the last set, no, when he start to miss, you know. I saw him a little bit, you know, suffering a little bit on court at the end. He's one of my best friends on tour. I feel very sorry for him."
Local favourite Jo-Wilfried Tsonga reached the French Open quarter-finals for the first time with a 6-4 7-6 3-6 3-6 6-4 win against Swiss 18th seed Stanislas Wawrinka.
The fifth-seeded Frenchman was 4-2 up in the decider when the match was interrupted by dusk on Sunday and dropped serve when play resumed on Court Philippe Chatrier on Monday.
Tsonga, the last Frenchman to reach a Grand Slam final - at the 2008 Australian Open - wrapped it up by breaking Wawrinka with a forehand winner after four hours and six minutes.
He will face world number one Novak Djokovic of Serbia on Tuesday for a place in the last four.
Juan Martin del Potro edged past Tomas Berdych in a battle of big-hitting baseliners to book his spot in the quarter-finals, winning 7-6 1-6 6-3 7-5.
After the match was suspended at the end of the third set due to bad light on Sunday evening, the ninth-seeded Argentine returned to wrap up victory in three hours 26 minutes.
"I got up (feeling) very positive and I restarted the match very focused and broke his serve, then he played better," Del Potro said.
"But in the end, I was really focused on winning the fourth set, and I did it in the last game, playing really well."
Del Potro exchanged clubbing flat forehands with his opponent in a first-set struggle that lasted over an hour before Berdych struck back emphatically in the second.
The Argentine, who will next play Roger Federer, returned to the ascendancy in Sunday's evening gloom before breaking decisively in the 12th game of the fourth set.
"I will walk on to the court with a very aggressive mindset; I want to play more volleys," Del Potro said about his quarter-final match.
Nicolas Almagro kept up the ruthless run by Spaniards as he reached the quarter-finals with a 6-4 6-4 6-4 hammering of Serbian eighth seed Janko Tipsarevic.
Almagro, the 12th seed, is one of three players in the men's draw yet to drop a set and kept the bearded Tipsarevic on his toes throughout the two hour 13 minute encounter and blew a kiss skywards after ending the Serb's ordeal with a driving forehand winner. Almagro will next face Nadal.
Ferrer was deafened but not stirred as he silenced shrieking Marcel Granollers with a 6-3 6-2 6-0 demolition job in their fourth round match.
While fans are accustomed to the likes of Maria Sharapova and Victoria Azarenka ratcheting up the decibel levels, Granollers proved that grunting was not confined to the women's game.
Unusually, Granollers often groans well after the ball has flown off his racquet but despite his antics, a focused Ferrer reached the last eight for the third time.
Sixth seed Ferrer has now won four straight-set matches, dropping only 25 games, and will be favourite to make it through to his first semi-final here when he faces either fourth seed Andy Murray or local hope Richard Gasquet.