The Germany international doubled Vincenzo Montella's men's lead shortly after half-time but the hosts scored to ensure they have hope
Juan Cuadardo fired them in front after 13 minutes with a stunning drive from an acute angle which gave goalkeeper Roman Burki no chance and the hosts were two down shortly after the break when Mario Gomez grabbed his first goal for his new employers in the opening leg of the play-off tie.
However, the Swiss side reduced the deficit through Anat Ngamukol and Montella admits, despite a satisfying performance from the Italians, that goal has given Grasshoppers a lifeline heading into the second leg.
“I had no doubts that this team would be ready with the right approach for a game like this,” Montella told Sky Sport Italia.
“It was unthinkable that we could all be at peak fitness right now and we could’ve finished the game off earlier, but the 2-1 result is good."
The Serie A season kicks off this weekend with Fiorentina hosting Catania on Monday. It was Montella's men's first taste of competitive football this season, having played a flurry of friendlies.
Fiorentina face the Zurich side next Thursday and the Italian knows they will have to shed their rustiness from pre-season if they want to reach the group stages.
“Grasshopper are dangerous on the counter-attack and it’s all still open, so we are not qualified yet. We did well and are satisfied with the performance," he added.
“This team can still improve and many of the lads have to grow, both in terms of fitness levels and their integration into the squad. For example, Cuadrado is very good, but I want him to be perfect.
“Giuseppe Rossi did well in attack and Gomez is always present in the box, though he can still do better. We are on the right path.”