Montanes, seeded 11th, defeated Teymuraz Gabashvili 6-2, 6-2 and won 57 percent of the points en route to the second round. But he had to battle for a 1 hour, 47 minutes to get there.
Montanes lost his serve just once but fought off another nine break-point chance He converted five breaks in 11 chances he created against Gabashvili.
No. 13-seeded Thomaz Bellucci was the only seeded player on Monday's card who didn't advance, losing 7-5, 6-3 to Santiago Giraldo. It was the third time in three career meetings that Giraldo beat Bellucci.
Guillermo Garcia-Lopez, seeded 12th, ousted Denis Istomin 7-6 (8-6), 6-3 behind five service breaks. Also No. 14 Kevin Anderson defeated Pablo Cuevas 7-5, 3-6, 6-4 while 16th-seeded Juan Monaco easily handled Grigor Dimitrov 6-4, 6-1.
The day's most lopsided decision Monday went to Pablo Andujar, who routed Gerard Granollers-Pujol 6-0, 6-1 in 58 minutes.
Other winners Monday were Albert Ramos, Blaz Kavcic, Robin Haase, Marcel Granollers, Benoit Paire, Victor Hanescu, Edouard Roger-Vasselin and Simone Vagnozzi.
Celebrity Families of 2014 [PHOTOS]