Montanes, the No. 7 seed, defeated Matthew Ebden 6-2, 6-3. Montanes won 52 percent of the points when receiving serve and finished with five breaks.
Cipolla, seeded eighth, took down Diego Junqueira 6-1, 6-4. He won 58 percent of the points both serving and receiving. The serving percentage is notable because Cipolla dropped serve three times.
Rui Machado beat Pedro Sousa 6-7 (3-7), 6-1, 6-2 in a battle of Portuguese players. Machado didn't lose his serve after the first set. He advanced to a second-round appointment with No. 1-seeded Juan Martin del Potro, the tournament's defending champion.
Another match pitting local players against each other saw Joao Sousa emerge a 5-7, 6-4, 6-2 winner over Gastao Elias, but Bjorn Phau stopped Portugal's Frederico Gil 6-4, 6-2.
Tuesday's other matches went to Spanish qualifiers Ivan Navarro, Inigo Cervantes and Daniel Munoz-De La Nava.
Swim Week Miami Beach 2014 [PHOTOS]