The former world number one, seeded 14, was too strong for the Czech, winning 6-2, 6-4 on Rod Laver Arena to set up a last-eight clash with seventh seed Kerber, who beat fellow German Annika Beck.
“She is such a tough opponent. I’m just happy I went through. I played smart, aggressive tennis,” said Belarus’s Azarenka, after being kept on court for one hour, 26 minutes.
“I’m feeling really happy and enjoying myself which helps me physically stay in shape. Barbora really pushed me and I’m happy I could stay focused and composed.”
Azarenka, 27, has been in the zone at Melbourne Park, dropping just 11 games in four matches as she zeroes in on another Grand Slam title after battling injuries for the past two years.
She went into the Strycova clash with a clear advantage, whipping her on all four of their previous meetings, including at the last two Australian Opens – 6-1, 6-4 in 2014 and 6-4, 6-4 a year later.
Melbourne Park has been a happy hunting ground for Azarenka, winning in 2012 and 2013. She has now made the quarters or better five times in her last seven attempts.
She said after her last match that part of her intensity and focus on court came from thriving on big-match pressure, a trait that served her well again Monday.
But it wasn’t straightforward against the dangerous Czech, who stunned third seed Garbine Muguruza in the last round to make her first fourth round appearance in Melbourne since her debut in 2004.
Both players held their opening serves before the Belarusian started finding space, creating four break points in the third game, but Strycova fended them off and held on.
It was only a temporary reprieve as Azarenka went on the attack with some piercing groundstrokes, giving her the first break of the match to pull 3-2 clear.
Azarenka, who hit the ground running this year by winning the Brisbane International, her first trophy since Cincinnati in 2013, was unrelenting and won the next three games to take the set.
Ranked 48 in the world, Strycova managed to resist the barrage of groundstrokes flying towards her as the second set got underway.
But the intense Azarenka, nicknamed “Vika”, kept plugging away and got the break she was after in the seventh game to pull 4-3 clear.
Despite some dogged resistance from the Czech, including two break points in the eighth game, Azarenka powered home to once again signal a clear threat to defending champion Serena Williams, who she could meet in the final.