The 22-year-old, ranked in the world Top 20 before being diagnosed with the cancer last May, rallied for a 2-6, 6-3, 6-2 victory over Sweden's Johanna Larsson in Day 1 of the Miami tournament.
Kleybanova advances to the second round where she will face No. 22 seed Maria Kirilenko of Russia.
Also Tuesday, former world No. 4 Jelena Dokic of Australia fell to Russian Ekaterina Makarova 6-1, 7-5 in an 80-minute match and Mona Barthel of Germany routed Hungarian Greta Arn 6-1, 6-0.
Meanwhile, Bulgarian Tsvetana Pironkova handled Petra Martic of Croatia 6-3, 6-2, and British wild card Heather Watson squeezed past Romanian Sorana Cirstea 6-3, 3-6, 7-6 (7-4).
Notable deaths of 2014 [PHOTOS]