The Serbian third seed stepped up his level to easily get past the Spanish 14th seed, 6-3, 6-4, 6-0 in 1hr 44min on a sweltering day at Hisense Arena.
Djokovic, who won the Australian title three years ago, will now take on either Czech sixth seed Tomas Berdych or ninth seed Fernando Verdasco of Spain in Tuesday's quarters.
He leads Berdych 4-1 and Verdasco 5-4 in previous meetings.
It is Djokovic's fourth straight Australian Open quarter-final and he has now reached the quarter-finals or better at 14 of his last 16 Grand Slam events.
"That was a higher standard than my previous matches and it's a big positive for me heading into the quarter-finals," Djokovic said.
Djokovic picked up a code violation in the third game of the second set for what the chair umpire said was making a signal, possibly to his coach.
When Djokovic approached the umpire to challenge his ruling he was heard to ask why he wasn't given a prior warning instead.
It was an impressive performance by Djokovic with five service breaks of the big-serving Spaniard along with 31 outright winners, offset by 17 errors.
His service game was on song with 12 aces, a 75 first-serve percentage and he cleaned up 86 percent of the first service points.
Djokovic swept through Almagro to love in the final set to seal a terrific performance as he heads into the second week of the season-opening major.