Kammala wannan jumla: Kozlov ya rubuta ta San Jose Sharks a zagaye na farko a matsayin na shida overall selection a cikin
Ƙaddamar da NHL na 1993. Kozlov ya zira kwallaye na farko a wasan Sharks da Ed Belfour da Chicago Blackhawks a ranar 21 ga Maris, 1995 a cikin rashin nasarar Sharks 7 zuwa 3. Zai buga wasu yanayi a San Jose kafin a siyar da shi zuwa Florida Panthers a ranar 13 ga Nuwamba 1997. Zai kasance a Florida, wasa tare da Pavel Bure, cewa Kozlov zai sami mafi kyawun shekaru. Mafi kyawun lokacinsa ya kasance ne a lokacin kakar 1999-2000 lokacin da ya kafa mafi girman aiki a cikin taimako da maki. Ya buga wasa tare da Panthers har zuwa 1 ga Maris 2004, lokacin da aka siyar da shi zuwa New Jersey Devils don Christian Berglund da Victor Uchevatov.