Malisse earned a break in the fifth game to clinch the opening set before the 124th-ranked Goffin, who lost in the second round last year, rallied to break in the sixth and eighth games of the second set, at the end of which Malisse complained of a stomach ailment.
Goffin closed it out in 1 hour, 53 minutes after securing the crucial break in the sixth game of the third set.
"He was sick I think ... (with a) stomach ailment. He was tired," Goffin said. "He is never easy to play, even if he is sick he can hit the ball very hard."
"It was one of the best matches I've played," 235th-ranked Sugita said of his victory over Rochus. "This is one of the highest-ranked players I've beaten."
Predominantly a baseline player, the 23-year-old Sugita counterpunched hard to keep No. 67 Rochus at bay.
Sugita said coming through the qualifiers helped him adapt to the conditions better, while Rochus was playing his first match of the new season.
"It was good for me," he said. "I hope to play this well in the coming rounds, and be prepared for the Australian Open qualifiers."