Fourth-seeded Gasquet of France beat unseeded Dick Norman of Belgium, 6-3, 6-4; No. 6 Grosjean beat fellow Frenchman Cyril Saulnier, 7-6 (7-5), 6-2; and seventh-seeded Malisse of Belgium topped France's Julien Benneteau, 6-2, 7-6 (7-5).
Among the losers this week at the upset-laden tournament were the top three seeds -- No. 1 Marcos Baghdatis of Cyprus, No. 2 Gaston Gaudio of Argentina and third-seeded Dominik Hrbaty of Slovakia.
In Sunday's final, the tournament's winner will pocket $120,000.
Swim Week Miami Beach 2014 [PHOTOS]