Monfils, a former world No. 7, continued his recovery from a knee injury with a 6-4, 6-2 humbling of Raonic on the grass courts of Gerry Weber Stadium.
He now moves on to the second round, as did Bosnian lucky-loser Mirza Basic, who pulled off a 7-6 (7-5), 3-6, 7-6 (7-5) upset of seventh-seeded Pole Jerzy Janowicz.
Meanwhile, No. 6 Philipp Kohlschreiber of Germany -- the 2011 Halle champion -- breezed past Argentine Carlos Berlocq 6-3, 6-1 and Latvian Ernests Gulbis got past Marcos Baghdatis of Cyprus 6-4, 3-6, 6-3.
Other first-round winners Tuesday included German wild card Cedrik-Marcel Stebe, German Tobias Kamke, Argentine Leonardo Mayer and Austrian Jurgen Melzer.