Both men struggled physically as air temperatures peaked at 39.9 degrees Celsius with reports of 69 degrees being measured down on the court surface.
But 12-times grand slam champion Djokovic, playing his first tournament for six months because of an elbow problem, was the more durable as he recovered from a woeful start to claim a 4-6 6-3 6-1 6-3 win and take his record over Monfils to 15-0.
The 14th seeded Serb will play Spain's Albert Ramos-Vinolas in the third round.
"It was brutal," Djokovic who wore a compression sleeve and employed a truncated service action, said.
"I thought, it is going to be a big challenge for both of us. Gael is one of the best athletes in our sport.
"It was about just hanging in there."
Monfils looked in danger of keeling over from the middle of the second set and throughout the third -- pleading with the match umpire to give them more than 25 seconds between points.
"I was dying on the court for 40 minutes," the 31-year-old told reporters later after having revived in a cold tub.
"It was really warm. It was tough to breathe. I think it was the hardest (conditions) I have played in.
"I tried to cool down. But even with the ice towel, the water, I think my body was super warm."
Djokovic was rumoured to have requested to play his match in the middle of the afternoon, despite the predicted heatwave.
But if it was supposed to earn him an advantage that plan quickly unravelled as he opened the match with two double faults and lost his first two service games.
He then broke back twice to level the set.
"They should put this in the washing machine and start again," Channel Seven commentator Jim Courier, twice an Australian Open champion, said on air about the scrappy nature of the opening exchanges.
It did improve but Djokovic, with coach Andre Agassi watching on, dropped serve again 3-3.
The former world number one wasted two chances to break back as Monfils served at 5-4 and was powerless to stop the elastic-limbed Frenchman taking the opening set with a volley after running Djokovic ragged.
Monfils hung in for the first seven games of the second set but was clearly in distress -- seeking out the shade behind the baselines to catch his breath between points.
Djokovic showed no mercy and broke for 5-3 before sealing the set on serve, at which point Monfils called the doctor and went off court to visit the bathroom -- leaving his opponent to roast on his courtside chair.
The third set was a non-event but Monfils burst back into life in the fourth and despite breaking for a 5-3 lead it was Djokovic who became flustered as he struggled to seal victory.
On his first match point Djokovic blazed a forehand long, then he had two fend off two break points, before another match point came and went with an unforced error.
Monfils saved a third with an angled forehand but Djokovic converted at the fourth attempt with a volley.
(Reporting by Martyn Herman; Editing by Amlan Chakraborty and Sudipto Ganguly)
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