Russia's Sharapova, the world number three, was stunned by Slovak Dominika Cibulkova, a day after the shock defeat of top seed Serena Williams.
In contrast, defending champion Azarenka marched on, blasting past young American Sloane Stephens in straight sets.
After crashing 3-6, 6-4, 6-1 to the 20th seed, Sharapova revealed she was carrying a hip injury, but refused to blame it for the loss.
"I mean, those aches and pains are expected when you spend a long time on the court. You just have to play through it," said the four-time Grand Slam winner.
She added: "I think it was just because I played a lot. This is only my second tournament back, so it was those types of things that are expected."
Sharapova only returned to the tour in Brisbane this month after a long layoff for a shoulder injury, and she endured two hard-fought matches in intense heat ahead of Cibulkova.
The Slovak had never been beyond the fourth round in six previous attempts in Melbourne. The win sets up a quarter-final against Romanian 11th seed Simona Halep, who beat Serbia's Jelena Jankovic.
"I was 100 percent sure I could win. I never doubted myself even when I lost the first set," said Cibulkova. "I knew what I needed to do. The most important thing is to believe in yourself."
Azarenka's 6-3, 6-2 defeat of Stephens set up an encounter against either fifth seed Agnieszka Radwanska or exciting young Spaniard Garbine Muguruza for a place in the semi-finals, where Halep or Cibulkova will await the winner.
The Belarusian hasn't dropped a set and is starting to hit top form as she moves deeper into the tournament with her winning streak at Melbourne Park stretching to 18 matches.
"It was a tough match but I was ready to battle for as long as it took," said Azarenka, who is well-placed to become the first woman to win the title in three consecutive years since Martina Hingis between 1997-99.
"I'm glad I could find my rhythm and go for my shots. I just love playing here. It feels so cosy, it feels like home," she added of Rod Laver Arena.
It was her first meeting with 20-year-old Stephens, the 13th seed, since their controversial last-four clash here in 2013.
During that match, Azarenka walked off court for a medical timeout after Stephens had saved five match points and broken the Belarusian.
She returned after a slow handclap from the crowd and Stephens won only three more points, losing 6-1, 6-4 and leading to accusations of gamesmanship. Azarenka later said she was troubled by a rib injury.
One of the tournament surprise packages so far has been Halep, who was voted the WTA's most improved player of 2013 and reached her first Grand Slam quarter-final by beating former world number one Jankovic.
Halep, who roared back from a mid-match wobble to win 6-4, 2-6, 6-0, said it was a dream come true to be in the last eight.
"Before the season I said my dream is to play a quarter-final in a Grand Slam. So my dream is true and I'm really happy," said the Romanian.
The result extends eighth seed Jankovic's long search for a maiden Grand Slam success. The 28-year-old is yet to improve on her runs to three semi-finals in 2007 and 2008.