Mario Gomez and Thomas Muller put Joachim Low's side 2-0 up before Hakan Balta gave Turkey hope by pulling a goal back with 10 minutes remaining.
Turkey will now be supporting Germany when they host the Belgians in Dusseldorf on Tuesday night, needing Low's team to at least get a draw to leave them a chance of finishing second with a win over Azerbaijan.
The first of those saves came in the fifth minute when he denied former Bayern man Hamit Altintop with an excellent instinctive save in a one-on-one situation.
At the other end, Germany did not look their usual selves going forward, with chances few and far between as the visitors seemed to take it easy early on.
They changed that attitude in the 35th minute, though, when another of Bayern's in-form players, Gomez, put then in front.
After making a save at the back, Neuer launched a quick counter-attack with a throw into the path of club-mate Muller, who in turn played the ball through for Gomez, who exuded confidence in the way he finished past Volkan Demirel having seen off the attentions of Servet Cetin.
Germany continued to wait for chances on the counter-attack and another quick clearance by Neuer set up Muller, but this time he shot over the crossbar.
Muller made it two in the 66th minute with Neuer again involved with a long clearance.
This time it was Mario Gotze who played the link-up man between the Germany goalkeeper and the forward as he played an inch-perfect pass into the path of Muller, who left Demirel no chance with a powerful shot.
The hosts, likely aware that Belgium had built a convincing lead against Kazakhstan, responded and found a way back into the game when Balta scored in the 79th minute.
Gokhan Gonul crossed from the right wing and Balta was left all alone to shoot past Neuer.
The provider of Turkey's goal then turned the villain as he fouled Muller in the penalty area and Schweinsteiger stepped up to send Demirel the wrong way and restore Germany's two-goal advantage in the 86th minute.