Rezai played for more than 2 1/2 hours in beating Arantxa Rus 4-6, 6-4, 6-3 and advancing to the second round. Rezai fought off 14 of 19 break points for Rus while finishing off seven of her own break-point chances.
The only other seeded player to secure a spot in the second round Tuesday was No. 2 Yaroslava Shvedova, who defeated Irina-Camelia Begu 6-3, 6-2.
Eighth-seeded Alize Cornet was ahead 6-3, 5-3 over Andrea Hlavackova when play was suspended because of darkness. Scheduled matches pitting No. 3-seeded Lourdes Dominguez Lino versus Melanie Oudin and Chanelle Scheepers against Polona Hercog didn't ever get started Tuesday. They will be played Wednesday.
Dinara Safina posted one of the most impressive showings Tuesday, routing Jill Craybas 6-1, 6-0 in 51 minutes. Safina won 70 percent of the points and didn't face a break point in improving to 6-0 in her career against Craybas.
Other first-round winners Tuesday were Alberta Brianti, Kirsten Flipkens, Anastasia Pivovarova, Kristyna Pliskova, Eleni Daniilidou and local favorite Nadia Lalami.
Swim Week Miami Beach 2014 [PHOTOS]