World number two Djokovic is vying to become just the eighth man in history to complete a career grand slam, but he was made to work hard against 25th seed Marin Cilic on the famous red clay of Roland Garros on Friday.
The Serbian needed four sets to defeat Cilic 6-3 6-2 6-7 (2-7) 6-4 on Court Suzanne Lenglen, and only hit 33 winners in comparison to Cilic's tally of 42.
However, Cilic was ultimately punished for making 64 unforced errors as Djokovic booked a date with Tsonga in round four.
Backed by a partisan home crowd, Tsonga was able to comfortably defeat Poland's Jerzy Janowicz 6-4 6-4 6-3 in just over two hours.
Tsonga, who is looking to better his run to the semi-finals 12 months ago, benefited from his opponent serving nine double faults.
Eighth seed Milos Raonic was involved in a back-and-forth five-set epic with Gilles Simon, the Canadian eventually triumphing 4-6 6-3 2-6 6-2 7-5.
Raonic was boosted by 60 winners, but also contributed 74 unforced errors in a thrilling encounter.
The 23-year-old will meet the winner of the clash between Marcel Granollers and Martin Klizan. Granollers led by two sets to one when bad light forced the match to be suspended.
Federer moved into the fourth round at the French Open for a record 12th time by beating Russia's Dmitry Tursunov 7-5 6-7 (7-9) 6-2 6-4.
The 17-time grand slam champion was pushed hard by Tursunov in the opening stages but stood firm to progress, and his 12th last-16 appearance at Roland Garros surpasses the 11 achieved by Argentina's Guillermo Vilas.
Latvia's Ernests Gulbis awaits the Swiss in round four, the 18th seed having comfortably beaten Radek Stepanek 6-3 6-2 7-5.
Tomas Berdych will face American John Isner for the right to contest the quarter-finals.
Sixth seed Berdych required four sets to defeat 27th seed Roberto Bautista Agut 6-1 6-2 6-7 (4-7) 6-4.
Isner was involved in a tight contest with Spain's Tommy Robredo, but the 10th seed eventually triumphed 7-6 (15-13), 7-6 (7-3) 6-7 (5-7) 7-5.