Volandri dispatched wild-card entrant Marko Djokovic 6-3, 6-1 in 60 minutes. Djokovic is the brother of world No. 1 Novak Djokovic, who won the Serbia Open last year but skipped it in 2012 because of the death of his grandfather.
Volandri lost just 14 points in his eight service games and didn't face a break point. He also won also half (24-of-49) of the points off Marko Djokovic's serve.
Volandri advances to a second-round match against top-seeded Pablo Andujar, who had a first-round bye.
Ivan Dodig had a pair of breaks in each set in getting past Adrian Ungur 6-2, 6-7 (4-7), 6-4. Dodig lost his own serve three times and the match took 2 1/2 hours to complete.
Serbia's Dusan Lajovic claimed a 7-5, 6-4 win over Evgeny Donskoy in a battle of wild-card entrants. Lajovic won 78 percent of the points on serve, losing 13 points over 11 games and not facing a break point.
Swim Week Miami Beach 2014 [PHOTOS]