Agassi, the No. 2 seed, was not at his best, but pulled off a 6-3, 7-6 (7-4), 6-3 win to move a step closer to a possible ninth Grand Slam title. He won Wimbledon in 1994 and '99.
"I'm doing what I need to do," said Agassi. "I need to get better."
Agassi is one of only two Grand Slam champions remaining in the men's draw after the exit of top-ranked Lleyton Hewitt on Monday.
Meanwhile, Serena Williams, the women's defending champion, struggled but beat Els Callens of Belgium, 6-4, 6-4.
Other winners were Tim Henman, David Nalbandian, Jiri Novak, Mark Philippoussis, Younes El Aynaoui, Juan Carlos Ferrero, Sebastien Grosjean, Justine Henin-Hardenne, Jennifer Capriati, Jelena Dokic, Elena Dementieva, and Mary Pierce.
Celebrity Families of 2014 [PHOTOS]