Fenerbahce found the first goal of the match in the 26th minute when defender Mehmet Topal scored with a header following a corner kick.
Giresunspor managed to equalize the score in the 73rd minute, thanks to a goal from Jones Carioca inside the six-yard box.
However, Fenerbahce was awarded a penalty kick in the 90th minute, when Giresunspor defender pushed striker Fernandao inside the penalty area.
Fernandao made no mistake to convert the kick into a goal to give his team advantage going into the second leg.
In the other match of the evening, Akhisaspor defeated Kaysersipor 1-0.