With Scotland’s play-off hopes dented in Tbilisi, group leaders Poland were knocked off the Group D summit by the world champions in Frankfurt.
Goals from Thomas Muller and Mario Gotze put Joachim Low’s side 2-0 up inside 20 minutes. Though Robert Lewandowski pulled a goal back, his Bayern Munich team-mate Gotze sealed the points late on with his brace.
Even with ground still to make up, Martin O’Neill’s Ireland will hope to catch Poland for the second automatic qualifying berth in the three-match run-in.
Poland had been warned about Germany’s attacking intent early on when only a deflection denied Karim Bellarabi from grabbing the lead.
It took just 12 minutes for their their defence to be left chasing shadows. A slick move down the inside left channel caught the Polish rearguard unawares and when Jonas Hector’s squared the ball across, left unmarked in the centre to sidefoot the finish home was Muller.
If that opener was impressive, then Gotze’s goal eight minutes later was even more so.
Excellent combination play from Toni Kroos and Karim Bellarabi was the precursor for the World Cup match winner skipping inside onto his favoured right foot and beating Lukasz Fabianski at his near post with a low drive.
Poland’s notoriously stubborn defence were getting stretched by the hosts’ expansive tactics and they were lucky not to concede a third when Muller broke clear only to be denied by the feet of Fabianski.
For the last 10 minutes of the first half, however, the visitors were dominant.
Left-winger Kamil Grosicki began to get the measure of debutant Emre Can and his incisive run and cross helped reduce the arrears on 38 minutes.
Lewandowski still had work to meet the wicked centre but his diving header from six yards carried enough power to beat Manuel Neuer despite him getting a hand to the effort.
Still, the next duel between the Bayern Munich pair went the way of Neuer.
Lewandowski seemed certain to equalise after haring through on goal unchecked but his thunderous volley caught the slightest of glances off the stopper’s glove to steer the ball over the crossbar.
Glad the half-time whistle stalled the Polish revival, Germany regained a foothold early in the second half with Gotze seeing his 57th-minute curling shot rebound off the post with Fabianski well beaten.
The open nature of the contest continued, though, as it took the reflexes of Neuer to keep out Krzysztof M?aczy´nski’s shot after the Polish centre-back was given too much space eight yards out.
It would be the Poles’ best chance of pinching a point as Muller and Gotze were to the fore once again for Germany’s third goal on 82 minutes.
When Gotze teed up Muller to shoot from 20 yards, there appeared little danger but Fabianski was wrong-footed by the drive and could only spill the rebound into the gleeful path of Gotze to tap home from close range.
Neuer; Can, Boateng, Hummels, Hector; Schweinsteiger, Kroos; Müller, Ozil, Bellarabi (Gundogan 53); Götze (Podolski 90).
Fabianski; Piszczek (Olkowski 43), Szukala, Glik, Rybus; Jodlowiec, Krychowiak, Maczynski (Blaszczykowski 63); Grosicki; Milik; Lewandowski.
Nicola Rizzoli (Italy).