Federer, 38, faced Hungary's Marton Fucsovics who managed to win the first set of the match. But the Swiss great hardly gave anything away after that and roared to a 4-6, 6-1, 6-2, 6-2 win. Federer will now face American Tennys Sandgren in the quarters on Tuesday.
Djokovic had a more straightforward path to the quarters. The 32-year-old beat Argentina's Diego Schwartzmann 6-3, 6-4, 6-4 to set up a match against Canadian Milos Raonic.
Sandgren got to the quarters with an intense 7-6 (7), 7-5, 6-7 (2), 6-4 win over Italian Fabio Fognini. Raonic, on the other hand, beat Croatian Marin Cilic 6-4, 6-4, 7-5.
World no.1 Ashleigh Barty will face world no.2 Karolina Pliskova in the quarters. Barty, looking to become the first Australian to win the title in Melbourne since Chris O'Neil in 1978, beat world no. 18 Alison Riske 6-3, 1-6, 6-4 while Pliskova beat Greek Maria Sakkari 6-7 (4), 6-3, 6-2.
American teen sensation Coco Gauff's run was stopped by her compatriot Sofia Kenin. Kenin won the match 6-7 (5), 6-3, 6-0 and set up a match against Tunisia's Ons Jabeur. Jabeur beat China's Qiang Wang 7-6 (7), 6-1 to become the first Arab woman to reach the quarter finals of a Grand Slam.
( With inputs from IANS )