Djokovic stretched his unbeaten record over Monfils to 15-0, one of the longest at Tour level, after dropping the opening set but just managed to get to the finish line.
He just did enough at the end to carve out a 4-6, 6-3, 6-1, 6-3 win in 2hr 45min on baking Rod Laver Arena.
The 12-time Grand Slam champion has a day to recover for his third round encounter with Spanish 21st seed Albert Ramos-Vinolas.
"It was brutal conditions and we both suffered, it was a big challenge for both of us," Djokovic said on-court.
"Gael is one of the best athletes in our sport but he was not at his best in the second and third sets. It was about just hanging in there and try to use every opportunity."
Asked about the state of his right elbow, Djokovic added: "It's still not 100 percent, but it's building. I have a lot of faith and belief in what I am capable of."
A decade after winning his first Melbourne Park title Djokovic has slipped to 14 in the world, his lowest in 10 years, but he has survived the opening two rounds in his comeback Grand Slam.
Monfils broke Djokovic's opening two service games to get off to a flyer, only to give back a break with a double-fault on break point.
Djokovic's greater consistency yielded a second break when Monfils hit a wild backhand, but the Serb 14th seed was broken a third time.
The Frenchman began showing the debilitating effects of the searing on-court temperatures and often was hunched with his hands on knees in between points.
He was broken in the eighth game and Djokovic served out for the set as the distressed Monfils sought the doctor and trainer during the changeover.
He complained of dizziness and left the court before returning for the third set.
Monfils went down a double break as he looked to be running on empty and Djokovic doing his best to keep things together.
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