The world number two, seeking his fourth consecutive title in Melbourne, cruised to a 28th straight win on tour with a comprehensive 6-3 6-0 6-2 success over the 15th-seeded Fognini on Sunday.
Djokovic served a statement of intent from the off at Rod Laver Arena, holding to love in his first three service games, although he sealed the opener with just a single break.
However, the Serb moved through the gears in set two, surging into a 4-0 lead with some sublime play that included a run of taking 14 points from 15 after being taken to deuce in the first game.
Overall, Djokovic - whose last defeat came to Rafael Nadal in September's US Open final - broke Fognini's serve six times and struck 33 winners to set up a quarter-final clash with Stanislas Wawrinka.
The eighth-seeded Wawrinka, who lost to Djokovic in a five-set epic in the fourth round of last year's Australian Open, overcame Tommy Robredo 6-3 7-6 (7-3) 7-6 (7-5).
The Swiss eased to the first set in relatively comfortable fashion, before 17th seed Robredo fought back to force tie-breaks in the second and third.
However, Wawrinka - who racked up 14 aces throughout the encounter - held his nerve to secure his spot in the last eight.
Earlier on Sunday, third seed David Ferrer battled back from a set down to beat Florian Mayer 6-7 (5-7) 7-5 6-2 6-1.
Unseeded German Mayer looked on course to move into a two-set lead when he recovered from 4-0 down in the second to draw level at 5-5 after taking the opener in a tie-break.
However, Ferrer - who hit 64 winners, compared to Mayer's 33 - responded by winning 14 of the next 17 games to storm into a meeting with seventh seed Tomas Berdych.
Czech Berdych put in a fine display to beat the big-serving Kevin Anderson 6-2 6-2 6-3.
Anderson fired down 16 aces during the match, but Berdych did not give up a single break-point opportunity to the 19th seed, while also making just 17 unforced errors in comparison to the South African's 30.