Die Mannschaft were handed the chance to take the lead when Jake Gosling brought down Jonas Hector inside the box and a penalty was awarded. Bastian Schweinsteiger took the spot kick, but saw his effort saved by Jordan Perez.
Adam Priestley raided forward on a counter-attack for the home side and managed to find space to fire a shot at goal, but his effort lacked power and was saved with ease by Roman Weidenfeller.
Gibraltar threatened again when they won a free kick 25 yards from goal, which Aaron Payas curled over the wall, and Weidenfeller had to be alert to make the save low to his right.
The home side fended off the threat of the German attack and reached the 25th minute without conceding, which is the longest they have staved off an opposing team since turning professional last year.
However, Germany went ahead in the 30th minute as Schurrle pounced on a mistake at the back from Ryan Casciaro and slotted the ball past Perez.
The home side had a precious chance to level the match almost immediately when Joseph Chipolina volleyed the ball into the path of Lee Casciaro, who fired at goal to force Weidenfeller into making a strong save.
Perez kept the scoreline down just before the break as he denied Mesut Ozil one-on-one. From the rebound, the keeper raced to his feet to keep Max Kruse's effort out, showing rapid reactions to tip the ball past the post.