They first played each other in 2005.
The six-time champion advanced with a clear-cut 6-2, 6-3, 6-3 win over Spanish 21 seed Albert Ramos-Vinolas in 2hr 21min on Margaret Court Arena.
Gasquet pulled off some fiery strokes that left even Federer surprised but the Swiss stayed put, went about with his usual elegance and untouchability during his service games and just waited for Gasquet to give in to the pressure.
He has beaten the Spaniard in all five career meetings, including in straight sets in the fourth round at the French Open last year.
We've played a bunch of times, it's a good match, and I'm looking forward to it. I expect it will be very tough.
It improved his Australian Open record to 88-13 in his 19th campaign Down Under.
"Los pueblos amazónicos nunca estuvieron tan amenazados como ahora", dijo el Papa
El Papa urgió a "romper con el paradigma histórico que considera la Amazonia como una despensa inagotable de los Estados sin tener en cuenta a sus habitantes".
Djokovic next faces Korea's Hyeon Chung on Monday for a place in the quarter-final.
"I did say the first two matches you're going to see who's doing well and not so well".
He was a little defensive when pressed on the nature of the injury.
He's also a fan of Australia after his visit, though he has one piece of advice for the country: 'I think driving on the wrong side of the road needs to be switched'. However, he fell in the semifinals to Roddick, in a final set tiebreaker leaving him a paralyzing 120 points behind Agassi.
Roger Federer at the Australian Open. "I understand there is a factor of tickets". The Austrian lost a tie-break in the opener but fought back to win 6-7 (6-8) 3-6 6-2 6-2 6-3.
Watson's side has improved from seventh to fifth while giving their net run rate a shot in the arm.
Kevin ilusiona al América de Cali
Dos desatenciones derivaron en los goles de Anderson Plata y Wilston Morelo que sentenciaron el encuentro antes del descanso. Este viernes en la noche, Millonarios y América de Cali se enfrentaron en el Estadio Nemesio Camacho El Campín.
World No 94 Marterer reached the third round with a 6-4 4-6 7-6 (7-5) 3-6 6-3 over Spanish veteran Fernando Verdasco. You never know what can happen.' Instead, they will play at night as second match of the night session on Rod Laver Arena.
But the form she showed in beating 14th seeded Latvian Anastasija Sevastova deserted her. He had a chance to take over the #1 ranking for the first time from Andre Agassi if he made it to the Montreal final.
The opening stand set the platform for skipper Shane Watson to blast his side to victory with an unbeaten 49 from 28 balls.
He will next play the winner of Friday's later match between Tennys Sandgren and Maximilian Marterer.
The world No.2 is chasing a milestone 20th grand slam title and his first back-to-back Australian Open titles since 2006-07. Garcia will play Madison Keys in the fourth round.
Earlier, Jamie Murray and Bruno Soares were frustrated to have been eliminated from the men's doubles by the Indian pairing of Leander Paes - who remains a force at the age of 44 - and Purav Raja.
Las dos Coreas desfilarán juntas en los Juegos de Invierno 2018
En esquí de fondo, Corea del Norte enviará tres deportistas, dos hombres (15 kilómetros) y una mujer (10 kilómetros). En Sochi 2014 ningún norcoreano se clasificó.
In 2001, the young Federer had international breakthrough in the Wimbledon Championships.