The hard-serving Raonic finished a 7-6 (3), 7-6(3), 6-3 victory over Ukraine's Illya Marchenko with an ace on Tuesday while Pospisil squeezed out a tense win over American Sam Querrey in three hours, 6-3, 6-7 (5), 2-6, 2-6, 6-4, 6-4.
Raonic, who lost the Brisbane final this month to Swiss star Roger Federer, fired 28 untouchable serves, his best at 228 km/h.
"I'm very happy with how I played," said Raonic. "I competed well and managed to get through."
"I'm hoping 2015 can be my year. I've put in a lot of work and I believe I can win a Grand Slam title. I've come here to play."
The Thornhill, Ont., player will face Donald Young of the United States in the second round of the Grand Slam tournament. Young beat Tim Puetz of Germany, 6-4, 4-6, 6-3, 6-2 to advance from the first round. Raonic beat Young twice last season, first in Washington, D.C., and then indoors in Basel, Switzerland.
Raonic concluded Tuesday's match with his trademark stinging serve, joining Monday winner Eugenie Bouchard of Westmount, Que., in the second round in straight sets.
Raonic said that his momentum from a final against Federer earlier this month has little to do with how he performs at the first Grand Slam of the season.
"This tournament, every tournament, the previous one has nothing to do with it," said Raonic. "I always start at zero. I have to find my way into it.
"That's something I've learned to accept, I wasn't the best at it before, especially the first few years on the tour. But it's just about getting through and giving myself an opportunity to play better in the next match."
Pospisil's match ended on a double-fault from Querrey, who had beaten the Vancouver native in their only other meeting.
Pospisil finished with 20 aces, 58 winners and broke on four of five chances.
He next faces Italian Paolo Lorenzi, who beat Alexandr Dolgopolov 6-4, 6-3, 6-2.