Raonic, from Thornhill, Ont., beat Ginepri in straight sets, 6-2, 6-2.
Wimbledon finalist Eugenie Bouchard of Westmount, Que., meanwhile, suffered another hard-court disappointment in losing to Russian Svetlana Kuznetsova 6-4, 3-6, 6-2. Earlier, Vancouver's Vasek Pospisil pushed Roger Federer to a third set before falling to the tournament's second seed.
Raonic says he was pleased with his performance, but is looking for improvement.
"I felt great after the first match of the week," said the Wimbledon semifinalist. "These were much different conditions than last week at the Rogers Cup.
"But I came up with the right mentality and was able to execute well. I wasn't particularly nervous. I knew how I'd prepared and what to expect. I was able to break right away and that made things go well form the beginning."
Bouchard played in her first tournament since Wimbledon last week, losing her first match at the Rogers Cup in Montreal.
She said Kuznetsova was a "tough opponent."
"I think Svetlana was pretty solid," she said. "For me, you know, it's still a work in progress."
She said the time off did contribute to the result.
"With all the time I took off and everything it would kind of be a long journey back to get back to where I was and to get better than that," she said. "But I feel better this week than last week, so that's a positive. It's all about moving forward."
Federer, third in the ATP world rankings, is coming off an appearance in the finals of the Rogers Cup in Toronto. Federer lost that match to Jo-Wilfried Tsonga.
The Swiss tennis star beat Pospisil 7-6 (4), 5-7, 6-2 in the second-round match on centre court to become the only man to reach 300 wins at the Masters 1000 level in men's singles.
Pospisil beat Radek Stepanek in the first round in Cincinnati a week after losing his opening match at the Rogers Cup. He had 33 winners and 37 unforced errors against Federer.
Pospisil played tough against Federer, forcing a tiebreaker that he ultimately lost on a forehand error. Pospisil secured the second set when Federer missed on a forehand cross-court.
The third set was all Federer, with Pospisil broken twice on the way to the loss.
"Any time you play Roger, there is always extra tension," said Pospisil. "I've always looked up to him so much. I was tense in the first set and that claimed a lot of energy.
"In the second I played better but in the third a couple of points made the difference."
Pospisil also pointed to his heavy playing schedule at Cincinnati as a problem.
"I had heavy legs at that point, maybe I was paying the price for the first set," he said. "I had five sets form singles and doubles the day before.
"I was missing some pop in my serve and he played well when he needed to."