Raonic, from Thornhill, Ont., defeated Bernard Tomic 7-6 (8-6), 6-1. The 23-year-old Canadian fired 18 aces, including two in the final game.
Montreal's Bouchard gave Canada the evening's winning point as she beat a grand slam champion for the third time in her career with a defeat of 2011 U.S. Open winner Samantha Stosur 4-6, 6-2, 6-3. She also beat former French Open winner Ana Ivanovic at Wimbledon last summer.
It was a promising start to the season for Raonic and Bouchard, who were respectively named The Canadian Press male and female athletes of the year earlier this week.
A mixed doubles tie was being played for pride at the Perth arena later.
Canada are competing at the event for only the second time after Frank Dancevic and Maureen Drake participated a decade ago.
Raonic ended his victory over Tomic in the pair's first meeting with an ace as he completed his opening match of the 2014 season a day after his birthday.
"It was really good, I'm proud of the things I did," he said. "I started off in the first set really well just tightened up a little bit. After the first set, I was a little bit more relaxed.
"The more the match went on the better my serve got. That's key to me obviously no matter how much I improve everything else that's going to be my key weapon."
Raonic and Tomic had never faced off on the ATP circuit despite coming from the same tennis generation, with both tipped as promising newcomers when they turned professional. The promise is being fulfilled for Raonic, while Tomic is stuck in the 50s on the ranking list and lost his last five matches of 2013.
Raonic had to fight through a 52-minute opening set, but fired up his jets in the second as he dominated on the way to the win.
"I changed it up a little bit in the second set, but it was more him dropping off a little bit," he said. "He made some errors, and I was also putting a bit more pressure."
Bouchard, the WTA No. 32, lifted her record over Stosur to 2-1 after a battle of momentum shifts lasting for well over 90 minutes. The second set, when Bouchard began making her comeback, was marred by five straight breaks of serve before the 19-year-old Canadian took command.
"The second set was totally different than the first," Bouchard said. "I was trying not to let her control the point, especially with her great forehand, I put pressure on her and sometimes she would make the error.
"Things felt a bit rusty after taking three weeks off after my last match in October and then training for five weeks in Florida. But I'm glad I was able to make a good start to the season."
In the other opening day tie, Poland beat Italy 3-0 and will face fourth-seeded Canada on Sunday.