Belgium's Malisse, who was visibly angered by a number of calls made by the line judges throughout the four-set contest, made it difficult for the American who was appearing in front of a home crowd.
"I knew the match today was going to be tough," Isner told reporters. "A lot of people are projecting me to go far here, but I wasn't looking past this match.
"As you guys could see, I had my hands full. He doesn't mind playing me. He's played me well in the past and he did it again today. Got to a certain point there where it was anyone's match.
"I just got pretty fortunate at the end. I'm happy to move on."
Up next for the 27-year-old is a match against Jarko Nieminen.