Below, Sports Mole takes a look at the key talking points.
On target: 2
On target: 6
Was the result fair?
It is difficult to pile the misery on Scotland's passionate supporters, but the extra quality Germany possess in their side proved to be the difference on an entertaining evening in Glasgow. The first three goals were scrappy, before James McArthur levelled the match for the second time with a fine finish. Scotland enjoyed longer spells in possession in the closing stages, but they always lacked the cutting edge capable of slicing open the visiting defence. The best move of the match saw Gundogan fire home the winner, and it was a deserved victory for Joachim Low's side.
After the deserved criticism which arrived following the 1-0 loss to Georgia, this was the kind of display which restores faith in what Strachan is trying to achieve with this squad. Starting the game with a clear plan of keeping men behind the ball but pressing when Germany's defence had possession, Scotland were slightly unfortunate with the first two goals. However, a closer examination showed mistakes from McArthur and Charlie Mulgrew allowing Germany to get to the edge of the box, and it was the kind of space which Strachan must have been desperate not to give the away side.
Despite a couple of setbacks, Scotland refused to stray from their tactics and they fought back twice before the break to the delight of the Hampden Park crowd. After the interval, Germany were in charge for long spells and Scotland were unable to keep tabs on the likes of Gundogan, Thomas Muller and Mario Gotze. As they chased the game in the closing stages, it became clear that Scotland did not have the attacking quality to create the opportunities required. An improved display against the best side in the world should renew confidence, but a performance such as this one makes the defeat to Georgia even harder to forget.
It may not be remembered as a classic performance from Germany, but the victory is further proof that this squad possesses world-class quality and resilience in equal measure. Shocked by two equalisers from Scotland, Low's side never panicked and persisted with the same approach which has delivered so much success. Bastian Schweinsteiger and Toni Kroos were key to keeping the visitors ticking over as they displayed excellent passing but also matched Scotland's aggressive midfielders in the battle for superiority.
Despite conceding twice, there was not too much for the defence to do on a night when the visiting back four were invited forward to take part in the early stages of attacks. As has always been the case, attacks win matches and with the aggressiveness and direct style of Muller's play perfectly combining with Gotze's clever passing and movement, the world champions always looked threatening. Unusually, some of the play in the final third of the pitch did not click but the visitors were intelligent enough to see out the game comfortably.
Sports Mole's man of the match
Thomas Muller: What more can you say about the Bayern Munich forward? Trusted to start the match on the right, Muller popped up in different areas of the pitch to give Scotland's defence a 90-minute headache. The deadlock was broken when his low strike deflected off Russell Martin, before he reacted quickest to head home the second of the match. Despite also being a great help defensively, Muller earns his impressive reputation for his work in the final third and he set up the winner with a fine pass for Gundogan to finish. Brilliant on and off the ball throughout the evening.
Manuel Neuer will not be pleased with himself for pushing the ball against Mats Hummels to gift Scotland their second equaliser, but in the context of the match, David Marshall must take this honour. Solid for most of the night, the Cardiff City goalkeeper should have done much better with an Emre Can strike, and his inability to push the ball to safety allowed Muller to head home from close range.
Bjorn Kuipers kept the game flowing and avoided any controversy. The Dutch official also did James Morrison a favour by not showing him a second booking after committing two fouls following his caution.
Scotland: Strachan's side will look to boost their qualification hopes when they host Poland for their penultimate Group D fixture on October 8.
Germany: The world champions can clinch qualification with a positive result against Republic of Ireland on the same evening.