Djokovic won in four sets 11 years ago and needed one fewer this time, winning 6-3 7-5 6-4 as the clock ticked towards 1am.
Tsonga has slipped outside the top 100 in the rankings after missing most of last season because of knee surgery, but showed enough here to indicate he will soon be heading in the right direction.
Djokovic said afterwards he felt more nervous than usual because of his long history against Tsonga, calling him “one of the greatest rivals that I had throughout my life”.
Fourth seed Alexander Zverev survived another lengthy battle at a slam, staving off a fightback from Jeremy Chardy to win 7-6 (5) 6-4 5-7 6-7 (6) 6-1.
Stan Wawrinka and Milos Raonic are both working their way back up the rankings after injury problems and contested a high-quality encounter on Rod Laver Arena, which went the way of the Canadian 3-1.
In the women’s draw, Serena Williams eased to victory over Eugenie Bouchard to reach the third round, while Simona Halep survived another scare.
Williams is the 16th seed but very much the title favourite, easing to a 6-2 6-2 victory and will now meet 18-year-old Ukrainian Dayana Yastremska.
Having survived a first-round test against Kaia Kanepi, Halep looked to be finding things more comfortable against young American Sofia Kenin as she moved a set and 3-0 ahead.
But 20-year-old Kenin fought back to take the second set and led 4-2 in the third only for Halep to win 6-3 6-7 (5) 6-4.