Raonic dispatched Aussie Matthew Ebden 6-2, 6-4, 6-4.
Raonic is the eighth seed in the men's draw. The Thornhill, Ont., native is coming off his first quarter-final appearance at a major, at the French Open earlier this month.
He has never made it past the second round at All England Club, and will next take on either Jack Sock of the United States or Frenchman Pierre-Hugues Herbert.
Frank Dancevic of Niagara Falls, Ont., cut down six-foot-ten Ivo Karlovic on Croatia 6-4, 7-6, 7-6. Dancevic only qualified for Wimbledon last week as a so-called lucky loser when another player withdrew due to injury.
Dancevic will next take on either Dudi Sela of Israel or Mikhail Kukushkin of Kazakhstan.
Eugenie Bouchard of Westmount, Que., faces Slovakian veteran Daniela Hantuchova later Tuesday.
Bouchard is the only woman this year to reach the semifinals of both the Australian Open and French Open, and hopes to take the next step into her first ever Grand Slam final. She is the No. 13 seed.
Toronto's Sharon Fichman was eliminated Tuesday, 6-1, 6-3 at the hands of Timea Bacsinszky of Switzerland.
In early Tuesday results, Roger Federer defeated Paolo Lorenzi of Italy 6-1, 6-1, 6-3 to begin his quest for a record eighth Wimbledon title.
Federer, also attempting to win his 18th Grand Slam title, lost in the second round here last year, his earliest defeat at Wimbledon since 2002. He finished Tuesday's match with his ninth ace. It is Federer's 16th consecutive appearance at Wimbledon and his 59th Grand Slam event in a row, extending his record for the longest streak of consecutive majors in the Open Era.
Australian Open champion Stan Wawrinka advanced to the second round with a 6-3, 6-4, 6-3 win over Joao Sousa of Portugal.
Wawrinka, who served 18 aces, lost in the first round at the French Open in his first Grand Slam since winning his inaugural major at Melbourne in January.
The Swiss player had had lost five times in the first round at Wimbledon, including the past two years.
Jo-Wilfried Tsonga needed just four points and two minutes to complete a five-set victory over Jurgen Melzer.
The 14th-seeded Frenchman was set to serve for the match at 5-4 in the deciding set when rain forced a suspension and eventually a postponement of the first-round match Monday.
Tsonga, a two-time semifinalist at Wimbledon, came back out Tuesday and held serve at love, finishing with his 20th ace, to complete a 6-1, 3-6, 3-6, 6-2, 6-4 win.
Last year's runner-up, Sabine Lisicki of Germany, advanced to the second round at Wimbledon on Tuesday with a 6-2 6-1 win in less than hour over Julia Glushko of Israel.
No. 20 women's seed Andrea Petkovic of Germany advanced past Poland's Katarzyna Piter, 6-1, 6-4.