With Andy Murray, Juan Martin Del Potro and Tomas Berdych all falling to lower-ranked opposition on Thursday, Djokovic lost the first set to the Argentine 14th seed as he appeared to struggle with the ankle injury that threatened to rule him out of this tournament.
But the Serb showed just why he is the undoubted best player in modern tennis by adjusting his game, finding a second wind, and delivering some of his trademark agile slides and power returns to fly past Monaco into the last eight.
Djokovic will face Jarkko Nieminen for a place in the semi-finals after he beat world number five Del Potro in a three-setter.
"It was very difficult for me today," Djokovic said.
"Another tough match. I am trying to take things day by day. I didn't know what to expect today and I'm really glad that I won."
Juan Martin Del Potro lost an engrossing contest 4-6 4-6 6-7(4) to Jarkko Nieminen, while Fabio Fognini ousted Tomas Berdych with an excellent 6-4 6-2, although favourite Rafael Nadal moved through with little fuss.
Del Potro was ousted by an inspired performance from Finn Nieminen, who played some marvellous winners from all over the court in an all-action retrieving masterclass in the day's final match.
The fifth-seeded Argentine responded to losing the opener with an excellent second-set recovery but, after a frenzy of breaks and break-backs, failed to serve out a ding-dong decider that went to a tie-break.
Nieminen, the 31-year-old world number 49, saved the best for last though, taking the tie-break 7-4 thanks to some incredible brave and accurate winners under pressure.
Fourth seed Berdych traded breaks with Italian Fognini early on but fell to pieces after a vital break at 4-4.
Fognini - whose forehand was too much for Berdych at times - went on to dominate the rest of the match, breaking the error-prone Czech twice in the second set before serving it out in style.
Reigning champion Rafael Nadal notched up his 44th win in a row in the principality over Philipp Kohlschreiber 6-2 6-4 and set up a quarter-final encounter with 34th-ranked Grigor Dimitrov of Bulgaria.
German Kolschreiber did not pose a big threat to Nadal, who had taken a month-long break to rest his knee after making an impressive comeback to the tour from seven months out injured by winning three titles including the Indian Wells Masters last month.
The Spaniard pleased the big crowd with a solid display on the sun-baked Centre Court that has been his stage since 2005.
"The match started with a lot of intensity for both of us and I was able to have the break. After that, I was comfortable with my serve," Nadal said.
"The second set, I think the intensity went down a little but I was in control," he added.
Dimitrov, who at 21 is making his debut in the Monte Carlo main draw, beat German Florian Mayer also by 6-2 6-4.
Tsonga eased into the quarter-finals with a dominant 6-3 6-0 win over Juergen Melzer.
The Frenchman’s forehand and athleticism were too much for the Austrian, who was broken at the second time of asking in the first set before being utterly blown away in the second.
Tsonga, who won in less than an hour, will face Wawrinka for a place in the last four.
Results from the Monte Carlo Masters Men's Singles
Round 3 matches:
Jarkko Nieminen (Finland) beat 5-Juan Martin Del Potro (Argentina) 4-6 4-6 6-7(4)
1-Novak Djokovic (Serbia) beat 14-Juan Monaco (Argentina) 4-6 6-2 6-2
13-Stanislas Wawrinka (Switzerland) beat 2-Andy Murray (GBR) 6-1 6-2
3-Rafael Nadal (Spain) beat 16-Philipp Kohlschreiber (Germany) 6-2 6-4
Grigor Dimitrov (Bulgaria) beat Florian Mayer (Germany) 6-2 6-4
Fabio Fognini (Italy) beat 4-Tomas Berdych (Czech Republic) 6-4 6-2
6-Jo-Wilfried Tsonga (France) beat Jurgen Melzer (Austria) 6-3 6-0
7-Richard Gasquet (France) beat 9-Marin Cilic (Croatia) 7-5, 6-4