Malisse scored seven aces and broke a four-match losing streak while advancing to the next round of the Los Angeles tournament.
Marinko Matosevic, the No. 6 seed, rallied to beat Chris Guccione 3-6, 6-3, 6-3.
Also advancing Tuesday were Australian Matthew Ebden, Michael Russell of the United States and Igor Andreev of Russia.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys