The maiden MotoE campaign was originally scheduled to start in May at the Spanish Grand Prix, but a fire in the paddock during testing in March at Jerez wiped out the entire fleet of electric motorbikes.
It was then decided to postpone the opening race until Germany.
Eighteen riders lined up at Sachsenring, all competing on the same zero-emissions Energica electric motorcycles.
The bikes have no clutch or gearbox and have a top speed of 250kph.
Tuuli started from pole and beat Briton Bradley Smith into second, with France's Mike Di Meglio third.
Initially meant to run for seven laps, a crash that damaged a barrier saw the race red-flagged after only five circuits.
Spain's Maria Herrera, the only woman in the race, finished 16th of the 18 riders.
The second race of the season will be held at the Austrian Grand Prix on August 11 with another four to follow.
Formula E, the electric answer to Formula One, has been running since 2014.
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