In one of the best matches of the opening rounds, the 196 cm (6.43 ft) Canadian repeatedly served his way out of trouble against an opponent armed with an elegant as well as destructive single-handed backhand.
The reserved Canadian raised his fists in triumph after his Swiss opponent misfired on his forehand on match point after four hours of intense play.
"Sort of just held on, got through," Raonic said. "Was a little bit lucky there, as well."
Raonic, seeded 16, will play Pierre-Hugues Herbert in the third round, after the French player beat last year's semi-finalist Chung Hyeon.
Neither Raonic or Wawrinka could assert authority in the early stages of the match, which resulted in a first set tiebreak, where Raonic secured a mini-break early on.
The Canadian had a straight-forward volley that would have extended his lead in the shoot-out but tried to wrong-foot his opponent, hitting the volley behind Wawrinka to his backhand.
This is a bit like giving spinach to Popeye.
The Swiss obliged, unleashing one of the most beautiful shots in tennis, a backhand forged near Lake Geneva in his home-town of Lausanne, that left the Canadian stranded.
Wawrinka followed up with a clean down-the-line backhand winner from the baseline the next point and soon secured the set.
Play was briefly halted in the second set as paramedics looked after a spectator who appeared to be struggling in the intense humidity.
The rain eventually came, and the centre court roof was closed for the first time this tournament.
Raonic's serve dominated the second set tiebreak, while the third set tiebreak turned into a tussle, as the Canadian's return-of-serve went missing, as did Wawrinka's first serve.
Wawrinka played a loose point at 11-11 in the tiebreak, giving the Canadian a chance to missile his way into a two-sets-to-one lead, which he did, by sending down another unreturnable serve.
"For sure, when it's that tight, the match can change for one, two points," said Wawrinka.
Wawrinka grabbed a break in the fourth set by landing a series of returns at the shoelaces of his incoming opponent and the match suddenly looked destined to go the full distance.
But Raonic recovered again to set up a fourth consecutive tiebreak and it took an wayward Wawrinka forehand to end the enthralling contest.
Wawrinka, a three times major winner who broke through to win his maiden Grand Slam in Melbourne in 2014, said he was pleased with his progress from a career-threatening knee injury last year.
"I have to keep pushing and keep doing the right things," he said.
"The season is long - 11 months. There is a lot of tennis to be played. Hopefully I will achieve some things."
(Reporting by Jonathan Barrett in Melbourne; editing by Amlan Chakraborty)
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