Federer, a four-time champion in the year's first major tournament and seeded sixth this year, defeated Tomas Gabashvili 6-2, 6-2, 6-3 while the 10th-ranked Tsonga, who lost in the 2008 finals in Melbourne, took out 18th-seeded Gilles Simon in third-round play.
Federer owns a 9-4 career edge over Tsonga, including a five-set win in the quarterfinals at last year's Australian Open. Tsonga was a strong straight-set winner at the French Open in his most recent match against Federer.
Conditions were much more favorable Saturday with a heat spell snapping, leaving temperatures in the comfortable 70s Fahrenheit. Highs the previous four days ranged from 104-109 degrees Fahrenheit.
Federer had just 18 unforced errors in his win over Gabashvili. Federer also saved all five of the break points he faced and took 87 percent of the points when his first serve was good. It is the 13th consecutive year Federer has advanced to at least the fourth round in Melbourne.
Tsonga fired off 17 aces and didn't have a double fault in a 7-6 (7-5), 6-4, 6-2 win over Simon. Tsonga didn't lose his serve, fighting off three break points.
Top-seeded Rafael Nadal completed the third round with a 6-1, 6-2, 6-3 win over 25th-seeded Gael Monfils. Nadal saved all six break points Monfils managed and won nearly two-thirds of the points on serve. He also had six breaks and took half the points off Monfils serve.
Fourth-seeded Andy Murray didn't allow a break chance after the first game in a 7-6 (7-2), 6-4, 6-2 decision over 26th-seeded Feliciano Lopez. Lopez opened the match with a break but Murray quickly answered and was solid the rest of the way.
A pair of unseeded players reached the fourth round with Roberto Bautista Agut, who defeated fifth-seeded Juan Martin del Potro in the second round, eliminating 27th-seeded Benoit Paire 6-2, 6-1, 6-4 and Stephane Robert topping Martin Klizan 6-0, 7-6 (7-2), 6-4.
Grigor Dimitrov, seeded 22nd, also advanced in an upset, taking out 11th-seeded Milos Raonic 6-3, 3-6, 6-4, 7-6 (12-10) while winning 80 percent of the points on serve. No 16-seeded Kei Nishikori handled Donald Young 7-5, 6-1, 6-0.
That put Nishikori in the fourth around against Nadal, who has lost only one set in building a 5-0 series record against Nishikori. Dimitrov and Bautista Agut play in the other fourth-rounder in that section of the draw.
The pairing opposite the Federer-Tsonga fourth-round match has Murray going against Robert.