The first leg of the two-legged tie started with a low tempo as both teams were looking to gain advantage by passing and building up attacks.
At minute 45, Fenerbahce's winger Jeremain Lens quickly used the set piece to set up Fernandao, and the Brazilian striker made no mistake from close range, giving his team the lead.
In the second half, Fenerbahce managed to control the pace and found another goal in the 71st minute, again with Fernando finishing from the six-yard box. Kayserispor, looking dismantled after being down 0-2, made a mistake and scored an own goal at minute 76 to a Fenerbahce cross, granting the Istanbulite giants an easy 3-0 victory.
The second leg will be played in Fenerbahce's home turf Ulker Stadium on April 5.
Other Turkish Ziraat Cup results:
Tuesday
Kasimpasa - Caykur Rizespor: 2-0
Wednesday
Sivasspor - Atiker Konyaspor: 0-0
Medipol Basaksehir - Akhisar Belediyespor: 1-1