A first-half double from Thomas Muller set Joachim Low's team on their way following a solitary point from their previous two matches in Group D.
Mario Gotze scored his first competitive international goal since netting the winner in July's FIFA World Cup final, but the atmosphere for what amounted to a game of attack against defence was a far cry from that heady night in Rio de Janeiro.
A Yogan Santos own goal ended an impressive spell of second-half resistance from Gibraltar, who have now conceded 21 goals in four European qualifiers.
Liam Walker almost had a moment to remember when he came close to scoring for the visitors with an audacious volley and it was to their credit that Germany's own European qualifying record victory of 13-0, recorded against San Marino in 2006, was never remotely under threat.
The home team established their expected dominance from the kick-off as Muller dragged wide on the end of Sami Khedira's backheel and the latter's Real Madrid team-mate Toni Kroos rippled the side-netting.
Jamie Robba saved well from Karim Bellarabi in the ninth minute, but the Gibraltar goalkeeper was at fault when Muller opened the scoring three minutes later - misjudging Shkodran Mustafi's cross that came back off the post and fell kindly for the in-form Bayern Munich forward.
Jerome Boateng clipped the outside of the far post from range in the 22nd minute before Jean-Carlos Garcia almost put through his own goal off Bellarabi's low cross.
Muller had his second in the 29th minute when a perfectly weighted pass from Gotze set Lukas Podolski clear down the left channel and he slipped the ball inside for the striker to finish.
Creator turned scorer after 38 minutes as Gozte neatly exchanged passes with Max Kruse to slot home.
There was almost a sensational goal for the visitors a minute before half-time when Gibraltar's Walker hooked a volley goalwards from 35 yards that forced a back-pedalling Manuel Neuer to save.
Khedira came close to turning home a corner early in the second half, but Germany's attacks began to lack tempo and Gibraltar's dogged defending reduced them to largely speculative efforts.
Low's men eventually found their way through again in the 67th minute as Podolski darted past Garcia and his low ball across the face of goal was turned in by Santos.
But Germany would not trouble the 7-0 margins already chalked up against Gibraltar by group rivals Poland and the Republic of Ireland on a night that will not linger long in the memory.
