Tenth-seeded Raonic, playing for the first time in more than a month after suffering ankle ligament damage, fired a modest 10 aces in a 6-4, 6-3 defeat of Colombian Alejandro Falla with a break per set providing the winning margin.
"I'm playing well this week, better with each match," said the 11th-ranked Thornhill, Ont., native. "I'm proud to be back on court again. I'm happy to be back and really happy to be playing so well, so quickly."
Raonic lined up a match against Wimbledon champion Andy Murray, who struggled to beat Czech Jiri Vesely 6-7 (2), 6-4, 6-4. Raonic owns a 2-1 lead in that series, winning their last in a 2012 Tokyo semifinal.
"I have got to go out there and play well, that's the main thing to focus on," said Raonic. "I have to really take care of my serve, and try to sort of make the most of the situations as they occur.
"Andy's in a situation where he didn't play for a big chunk of time (back surgery) and I'm in mine. I have to really buckle down and focus on myself and make sure I do my things well, and then change a few things that I may need to facing him."
Wozniak is making quick progress after a shoulder injury with a 6-1, 6-7 (3-7), 6-0 defeat of Russia's Anastasia Pavlyuchenkova.
The Blainville, Que., native set herself up for a huge test in the next round. She will face world No. 2, top seed and Australian Open champion Li Na after the two-time Grand Slam winner beat Czech Karolina Pliskova 6-3, 6-4.
This event marks the first time since late 2012, when her shoulder problems began, that the No. 241-ranked Wozniak has gone past the second round at a WTA-level tournament.
Wozniak was pleased to advance after fighting and losing a second-set tiebreak but dominating in the final set to sweep to victory.
"I"ve had a tough year and a half with my shoulder," she said. "It was a good match for me today. Russians are always tough, I had to being my 'A' game today."
Wozniak claimed victory in just under two hours, committing 10 double-faults in the match but breaking on nine of 13 chances.
Wozniak credited her French coach Nathalie Tauziat with helping her to the victory.
"She gave me encouragement and a boost for the third set," Wozniak said. "I was playing a little too far back on the court in the second. My balls were not as deep as in the first.
"In the third, I tried to step up more, take the ball early. I didn't want to let her get back into it like I did in the second set."
Wozniak, who will move into the 180s on ranking according to WTA estimates, is pleased with her comeback, which has bloomed this week in the desert.
"It's really good, I'm happy, I'm progressing with every match, step by step," she said. "I'm finding that aggressive way I used to play. It gives me confidence to start finding my game like before."
Wozniak will next play Li for the fourth time, standing 1-2 in the series.
"It's a privilege to play her," Wozniak said. "I'll have to play the way I know I can, like I've played this week. She loves to dictate from the first ball. I'll stay on her and try to have a good match.
"I won't be any more nervous than usual. I know how to handle these situations because I've been in them before. It will be important to start from the first point and stay with her in the rallies."