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.
In the second half, Germany doubled their lead when Ozil raided down the flank and managed to cut the ball back into the middle for Kruse, who was left with a simple finish.
Ilkay Gundogan added a third goal for Die Mannschaft as he capitalised on a deflection to continue his run into the box before burying the ball past Perez.
Germany secured a fourth when Ozil was again the architect, picking out the run of Karim Bellarabi and the midfielder held his composure to slot the ball into the net under the body of Perez.
Gundogan was crucial in his side's fifth goal of the evening as he surged right through the middle of the Gibraltar defence and fired an effort at Perez, who saved well, but Schurrle was on hand to tap in the rebound.
Schurrle completed his hat-trick in the 72nd minute when he latched onto a pass from Ozil and tapped the ball beyond the reach of Perez into the net.
Joachim Low's men completed the rout in the 82nd minute as Kruse scored his second goal of the match with a volley which gave Perez no chance as Germany eased to victory.