Fenerbahce hit the post three times before they belatedly made the breakthrough against their Portuguese rivals through Egemen Korkmaz with 18 minutes to go
For a long time, it appeared as if it would not be the Turkish oufit's night, having been denied by the woodwork three times, with Cristian even striking the post with a first-half penalty.
However, the hosts eventually made the breakthrough with 18 minutes remaining through Egemen Korkmaz, who headed home, almost inevitably, via the left upright.
"It is a great night for Turkish football," Kirt told reporters after the game. "We won in spite of our bad luck.
"Tactically, and in terms of preparation, we were incredible. We managed to cancel them out, having spent the last three days studying everything that they do."
Coach Aykut Kocaman was delighted that his troops had kept a clean sheet, though he was quick to acknowledge that the tie is far from over.
"It was very important for us not to concede, and we managed that today," the Fenerbahce boss enthused.
"Physically, I think we showed our strength tonight and we have managed to secure an advantage for the second leg.
"The final is by no means certain but we will do our best to make it. For now, I would just like to congratulate all of my players."
Aykut also insisted that he would not be taking the penalty-taking duties away from Cristian in light of his miss just before the break.
"It's meaningless to discuss this topic," he argued. "Penalties are missed. Cristian's our number one penalty taker and he will continue to take them."
Meanwhile, goalkeeper Volkan Demirel believes the unwavering belief within the squad was key to their success on the night.
"We played really well today," Volkan told reporters. "I congratulate my team-mates and our coach.
"We have again showed everyone what we can do and what you can achieve when you believe."
Defender Joseph Yobo was just as thrilled with the win and felt that Fenerbahce were good value for the 1-0 advantage that they will take to Lisbon next week.
"Benfica are a very good team, but we are also a good side, and we showed everyone that we can play tonight," the former Everton centre-half said. "It was a very good win."
Fenerbahce, who defeated Lazio in the quarter-finals, are making their first appearance in the last four of a European competition.