The ninth seed from the United States sent the wildcard and popular former champion from Switzerland spinning out 7-6(5), 2-6, 6-4, 6-4.
Wawrinka, who made his debut at Melbourne Park in 2006 and won the major in 2014, is playing his last season before retiring.
Fritz faces the fifth seed Lorenzo Musetti of Italy in the last 16.
"I've had so many emotions here the last 20 years because of you guys," three-time Grand Slam winner Wawrinka told the crowd, who had roared him on throughout.
"It's been an amazing journey. I won my first Grand Slam here and I always enjoy being back.
"I've always had so much support and the reason why I was still playing - it's because of you, because of the love of the game, the emotion you can give me."
There was nothing between Wawrinka and Fritz in the first set and they went to a tiebreak, where they exchanged a series of thunderous forehands.
With the roof closed at John Cain Arena because of the heat, the 28-year-old Fritz edged through in the first-set tie break.
Wawrinka, with the crowd firmly behind him, made a fast start in the second set to forge a 3-0 lead.
On Thursday, he became the first player aged 40 or over to reach the men's third round at a Slam since Ken Rosewall at the Australian Open in 1978.
He was exhausted afterwards and joked he might have a beer to celebrate.
But if Fritz was hoping there would be a hangover, he was to be disappointed.
Three-time Grand Slam champion Wawrinka saved two break points to go 5-2 up and broke Fritz to pocket the second set in 33 minutes.
Fritz fought back, triumphantly breaking in the seventh game of the third set with an enormous smash.
He was now in the zone and pulled away to move to within one set of victory.
The warhorse Wawrinka departed for a medical timeout after the third set as his Melbourne escapades caught up with him.
He was visibly wilting now as Fritz sealed his place in the second week.
Wawrinka, now ranked 139, peaked at world number three in 2014, winning the French Open a year later and the US Open in 2016.
The triumphs all came at a time when Roger Federer, Rafael Nadal and Novak Djokovic were dominating men's tennis.
Wawrinka has 16 career ATP titles, although the last came in Geneva in 2017.
He won Olympic gold in doubles alongside Federer at Beijing in 2008.