The top-seeded Djokovic routed the Frenchman 6-0, 6-1, 6-1 on Saturday to advance to the fourth round of the Australian Open. He needed only 1 hour, 14 minutes to dismiss the newly 30-year-old Mahut, who lost the longest match in Grand Slam history over 11 hours, 5 minutes against John Isner at Wimbledon in 2010.
"I wish him happy birthday, and hopefully tonight he can enjoy it," Djokovic said.
The defending champion is aiming to become the fifth man in the Open era to win three consecutive major titles. He next will play two-time Grand Slam winner Lleyton Hewitt, who reached the round of 16 in his 16th Australian Open after beating No. 23-seeded Milos Raonic of Canada 4-6, 6-3, 7-6 (5), 6-3 on his third match point in the night match.
Mahut was slowed by a left leg injury, but continued because the previous matches on Rod Laver Arena were over so quickly.
Djokovic has won 24 straight sets at the Australian Open, and has lost 10 games in his first three matches this time.
"I always played well in Australia. This is the only Grand Slam I won twice," he said. "The conditions are great. They're very suitable to my style of the game, day and night. I'm really looking forward to next week."
In all six Frenchmen reached the third round, but only two of them advanced. Tsonga wasted hardly any time becoming the first of them to move into the round of 16 and will next play Kei Nishikori of Japan.
Nishikori became the first Japanese man to reach the fourth round in Melbourne in the Open era with a 4-6, 7-6 (3), 7-6 (4), 6-3 win over unseeded Frenchman Julien Benneteau.
Richard Gasquet, the fourth highest-ranked Frenchman at No. 18, knocked out ninth-seeded Janko Tipsarevic 6-3, 6-3, 6-1. He will play fifth-seeded David Ferrer, who lost the first four games against Juan Ignacio Chela before recovering to win 7-5, 6-2, 6-1.
Information from The Associated Press was used in this report.