Raonic, who earlier spoke of his grief over a high school shooting in his home country, eliminated the Swiss world number four 6-4, 6-3, 5-7, 4-6, 6-3 and will face Gael Monfils in the quarters.
The 13th seed, who beat Wawrinka's fellow Swiss Roger Federer to win this month's Brisbane International, remains unbeaten this year after his impressive victory in three hours 44 minutes.
It was Raonic's first win against the reigning French Open champion in five meetings, and he has not lost a match at tour level since going down to Rafael Nadal in the third round of last year's Shanghai Masters.
Raonic, looking to take his game to another level under new coach Carlos Moya, was on track for a straight-sets win after four service breaks to lead by two sets in 76 minutes.
But Wawrinka lifted his intensity and took the match to a fifth set.
“It is more about what always comes down to me, trying to play in my rhythm, dictate and control the centre of the court and I thought like I was able to carry that through today,” Raonic said.
“It's the next step for me to try and achieve the goals I want to achieve and I am always looking at ways to get better and I am always working for that.”
The match turned in the third set when Wawrinka broke Raonic's serve in the 11th game and served out to keep the encounter alive.
Raonic started missing more and Wawrinka picked up his serving percentage, and he broke the Canadian in the fifth game of the fourth set and fought off four break points on his serve in the eighth game.
Wawrinka steamed to triple set point in the tenth game and took the match into a fifth set with the momentum shifting his way.
But in the final set, Wawrinka lost serve in a shaky sixth game when on second break point his forehand drive was just out, giving Raonic a 4-2 lead.
Wawrinka saved a match point in the eighth game but Raonic brought up a further three match points and finally won it with a put-away at the net.
Raonic, who dedicated his third-round win over Viktor Troicki to victims of last week's school shooting which left four dead, has yet to beat shotmaker Monfils in their two meetings so far.
TENNIS
Raonic fights off Wawrinka comeback bid
Canada's Milos Raonic fought off a comeback by 2014 champion Stan Wawrinka in a tense five-setter before taking a major scalp and reaching his second straight Australian Open quarterfinal on Monday.
ROGER FEDERER
Is this the end of the road for Swiss tennis legend Roger Federer?
Roger Federer is talking optimistically about returning to his "highest level" after knee surgery, but does tennis have to start adjusting to a future without the Swiss star?
The 20-time Grand Slam winner announced on Wednesday that he would be sidelined until 2021 after his second operation in a matter of months.
Federer remains upbeat, tweeting: “I plan to take the necessary time to be 100 percent ready to play at my highest level.”
In some ways 2020 is a good season to miss after the coronavirus ravaged the tennis schedule. Writing Federer off in the past has proved dangerous.
He returned from a six-month injury lay-off to claim the Australian Open in 2017, winning his eighth Wimbledon crown later that year.
But he will be 40 in 2021 and is now heading into uncharted territory.
Despite his groaning trophy cabinet, there are two factors that will motivate Federer to keep going — the risk of losing his grip on the men's Grand Slam title record and a missing Olympics singles gold medal.
Rafael Nadal has 19 majors, just one shy of Federer's mark and Djokovic has 17.
Spain's Nadal will be fancied to draw level with Federer at the French Open, rescheduled for September, while few would bet against Djokovic winning in New York weeks earlier.
In April, Federer said he was “devastated” when Wimbledon was cancelled for the first time since World War II. Last year he fell agonisingly short at the All England Club, failing to convert two championship points on his own serve against Djokovic.
The Wimbledon grass probably remains his best chance of adding to his Grand Slam collection — he has not won the US Open since 2008 and his only title at Roland Garros came in 2009.
Even though Federer has slipped from the very pinnacle of the game, he is still a major threat to Nadal and Djokovic.
'Golden' ambitions
Last year, the world number four had a 53-10 win-loss record and he reached the semi-finals at the Australian Open in January in his only tournament this year.
Federer, who is still six ATP titles short of Jimmy Connors' all-time record of 109, has one glaring omission from his CV — the Olympic title.
The Swiss won doubles gold in Beijing in 2008 with compatriot Stan Wawrinka but lost in the singles final to Andy Murray in London four years later.
The postponed Tokyo Games will almost certainly be Federer's last opportunity to complete a career “golden” Grand Slam — he will turn 40 on the day of the closing ceremony next year.
Tennis will feel the loss of the elegant Federer keenly when he walks off the court for the last time.
Djokovic and Nadal have been the dominant forces in recent years but the Swiss remains the biggest draw and last month topped Forbes' list of the world's highest-earning athletes.
His last appearance on court was in front of nearly 52,000 fans — touted by organisers as a world record for tennis — at a charity match against Nadal in Cape Town in February.
Federer is nearly always the crowd favourite wherever he plays and has proved a perfect ambassador for the sport since he won his first Grand Slam title in 2003.
He certainly expects to be back and competitive next year.
“I will be missing my fans and the tour dearly but I will look forward to seeing everyone back on tour at the start of the 2021 season,” he tweeted.
The avalanche of support from his adoring fans showed they would miss him too, but they will have to get used to a time when he is gone for good.
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