The Frenchman continued to impress on his return from a knee injury and, after breaking serve for 2-1 in the first set, he rarely looked troubled and quickly closed out a 6-4 6-2 win with an ace.
Monfils jumped from 119th to 67th in the world rankings last week after reaching the third round of the French Open, where he lost to Tommy Robredo.
Canada's Raonic has lost both his career meetings with Monfils and missed out on the chance to play qualifier Jan Hernych of the Czech Republic in the second round.
The other surprise result saw Bosnia's world number 240, Mirza Basic, beat seventh seed Jerzy Janowicz over three gruelling sets.
The 21-year-old lucky loser - only playing due to Philipp Petzschner's withdrawal through injury - finally triumphed 7-6(7/5) 3-6 7-6(7/5) when Janowicz of Poland sent a drop shot back long.
Basic's reward is an encounter with wildcard Mischa Zverev, while Cedrik-Marcel Stebe beat qualifier Jimmy Wang 6-2 6-4 to set up a second-round match against top seed Roger Federer.
Defending champion and third seed Tommy Haas awaits Latvia's Ernests Gulbis, who beat Marcos Baghdatis of Cyprus 6-4 3-6 6-3, while Leonardo Mayer recovered from 5-2 down in the first set to oust Germany's Jan-Lennard Struff 7-6 (7/4) 6-4, booking a date with namesake Florian Mayer.
It took Philipp Kohlschreiber just 56 minutes to beat Carlos Berlocq of Argentina 6-3 6-1 and tee up a match against fellow German Tobias Kamke, who made light work of Poland's Lukasz Kubot on his way to a 6-4 6-0 win.
Second seed Richard Gasquet of France awaits Jurgen Melzer after the Austrian sealed a 7-6 (7/5) 3-6 6-4 victory over Italian qualifier Riccardo Ghedin and Russia's Mikhail Youzhny, who defeated Daniel Gimeno-Traver of Spain on Monday, will tackle Japan's Kei Nishikori in the remaining last-16 tie.