The hosts were 15 minutes away from claiming victory, at the 15th attempt, only to denied by Okazaki's intervention.
Gertjan Verbeek's men made a bright start and moved ahead after just five minutes thanks to centre-back Per Nilsson's second goal of the season.
The Nuremberg supporters must have thought their side's winless run was set to end, but Okazaki had other ideas, latching on to a hopeful long ball and finishing calmly.
Mainz's goalscorer was withdrawn after his 75th-minute goal, but his replacement, Petar Sliskovic, failed to see out the game after receiving a straight red card in injury time.
Nuremberg remain 17th in the Bundesliga, while Mainz occupy seventh position.
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