Two goals from Thomas Muller and another from Mario Gotze put the world champions three ahead at the break, but only an own goal added to their lead as they perhaps failed to meet expectations in victory.
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Gibraltar conceded the 18th goal of their first competitive qualifying campaign when a cross from right-back Shkodran Mustafi fooled visiting keeper Jamie Robba by bouncing off the near post and into the path of Muller, who controlled and then converted the rebound.
Defender Jerome Boateng sensed an opportunity against the minnows to get himself a rare goal, and he curled a 20-yard shot narrowly wide of the post before forcing Robba into a save with a long-range drive.
Germany's attackers were enjoying themselves too and Muller made it two on 29 minutes. This time the cross came from the left as Lukas Podolski's drilled ball across the six-yard box was easily tapped home.
Muller was also involved in the third, as he exchanged passes with Bayern teammate Gotze on the edge of the area, before the latter wriggled into the box and found the bottom corner with his left foot.
Having not previously boasted a threat, Gibraltar nearly got on the scoresheet in spectacular fashion on 44 minutes when Liam Walker's 30-yard half-volley forced Manuel Neuer into a scrambling save.
Sami Khedira came within inches of nodding in a Mustafi flick on four minutes after the break, but Joachim Low's side had not registered a shot on target in the second half by the time that they went four up.
Walker tried his luck against Neuer again in the closing stages, but the Ballon d'Or nominee held his ferocious drive as Gibraltar remained goalless in four defeats with a result which sends Germany to second.