The odds were stacked heavily against the 28th seeded Pouille on his arrival in Melbourne after he lost all three of his singles matches for France in the Hopman Cup before making a first-round exit in Sydney.
Pouille exited in the first round in his five previous appearances at Melbourne Park and his quarter-final matchup was against an opponent who he had been unable to take a set off in three meetings.
On Wednesday, though, he simply dominated the 2016 Wimbledon finalist, facing a single break point over the entire match while earning 14 against Raonic, who is famous on the men's tour for his booming serves.
"I didn't have to face a break point for almost three hours," Pouille told reporters.
"Even if I lost the third set, in my mind it was clear I had to stay focused on my service game, taking care of that, then trying to put as many returns as I can.
"I'm still leading two sets to one, so I don't have to panic. I really needed to stay positive, still doing what I did great for two hours 30 minutes."
He passed Raonic with both forehand and lobbed winners and would have wrapped up the match in three sets if he had done justice to four break point opportunities in the third.
The 24-year-old hired former Australian Open and Wimbledon champion Amelie Mauresmo, Andy Murray's former mentor, as his coach recently and paid rich tribute to his compatriot after the victory.
"She knows everything about tennis. It's not about being a woman or a man. It doesn't matter," Pouille, a former top 10 player, said in an on-court interview.
"You just have to know what you're doing. And she does."
He took the first set with a brilliant forehand pass against an advancing Raonic in the tiebreak and converted his only break point in the second with a measured backhand lob before serving out emphatically.
The 28-year-old Raonic made Pouille pay for wasting the break points by winning the third set tiebreak but the Frenchman broke the Canadian again in the fourth, converting his third matchpoint to seal the contest in just over three hours.
Raonic has now lost three quarter-finals at Melbourne Park after exiting at the same stage in 2015 and 2017.
He sent down 11 more aces than his opponent but his serve was unable to get him out of trouble as Pouille won the crucial points.
Pouille will meet the winner of the last quarter-final between top-seeded Serb Novak Djokovic and Kei Nishikori of Japan for a place in Sunday's final.
(Reporting by Sudipto Ganguly; editing by Amlan Chakraborty)
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