It was a very tight match with just one break of serve that decided the outcome in the end.
Raonic will play Philipp Petzschner for a place in the quarterfinals.
David Nalbandian of Argentina also had to dig deep as he saved two matchpoints against Belgian Xavier Malisse to clinch the match 4-6, 7-6 (6), 7-6 (3).
Nalbandian won this tournament in 2008.
In other first round match, Kevin Anderson of South Africa ousted Guillermo Garcia-Lopez of Spain 7-6 (1), 7-6 (4).