The 23-year-old midfielder, who has now scored 11 league goals in this calendar year, struck twice after Hoffenheim took a 13th minute lead, first with a quick move in the box in the 18th and then with a superb shot into the top corner just after the hour mark.
The speedy German-Turkish playmaker, who is already a target for Turkey's national team, completed his hat-trick in the 68th minute after seeing his first close-range effort saved before drilling in the rebound.
Mainz move into third spot on nine points, with Hoffenheim, who have now lost four of their five games so far, in 15th place on one point.
Leaders Borussia Dortmund, with 12 points, host Bayer Leverkusen on Sunday while champions Bayern Munich, in second place also on 12, travel to promoted Darmstadt 98 on Saturday.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
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