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.
Walter Montillo se lesionó y Tigre revisará su continuidad
Montillo anunció su retiro en junio del 2017 luego de una seguidilla de lesiones musculares en Botafogo . Luego de que se le realicen los estudios, el club y el jugador definirán los pasos a seguir".
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.
Rafinha deja el Barça y se marcha al Inter de Milán
Rafinha Alcántara ya no será parte del Barcelona , al menos en esta campaña. En principio, firmaría por cuatro temporadas y media, hasta junio de 2022 .
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.
El Papa clama en Perú contra el saqueo, esclavitud y abuso sexual
El Papa Francisco no se refirió al indulto y tampoco accedió a reunirse con familias de las víctimas de abusos durante el Gobierno de Fujimori (1990 y 2000).
In 2001, the young Federer had international breakthrough in the Wimbledon Championships.