Joachim Low's world champions, who had laboured to a narrow 2-1 win over Scotland in their Group D opener, were below par and allowed Poland to clinch the points as they fell to a first competitive defeat in 19 outings.
The visitors fell behind to Poland's first effort on target early in the second period in Warsaw when Milik headed home from inside the area.
The Bayer Leverkusen man - who is on loan at Eredivisie champions Ajax - was later withdrawn to an enthusiastic ovation from the home crowd and, despite some tense moments for the hosts at the Stadion Narodowy, his replacement, Mila, made sure of the win with two minutes to go.
Germany threw caution to the wind late on as they looked to maintain a competitive unbeaten run that stretched back to Euro 2012.
However, it was to no avail as Poland picked up their first victory over Germany since unification to move top of the group, leaving Low with much to ponder ahead of Tuesday's visit of the Republic of Ireland.
Robbie Keane scored a 12-minute hat-trick as Ireland demolished Gibraltar 7-0 on Saturday, while an Akaki Khubutia own goal handed Scotland a 1-0 triumph over Georgia.
Albania missed out on the chance to go top of Group I as they were held to a 1-1 home draw by Denmark.
Gianni De Biasi's men claimed a shock 1-0 triumph in Portugal to get their campaign under way last month and looked set to to make it two wins from two on Saturday.
Ermir Lenjani put Albania ahead seven minutes before half-time, but Lasse Vibe levelled with just nine minutes left to play to ensure both sides are tied on four points.
Serbia's campaign got off to a lacklustre start as they drew 1-1 in Armenia, while the group's remaining side, Portugal, lost 2-1 to France in a friendly fixture.
Northern Ireland sit atop Group F at the end of matchday two, having beaten Faroe Islands 2-0 in Belfast to seal their best start to a qualifying campaign for 46 years.
Goals from Gareth McAuley and Kyle Lafferty in the opening 20 minutes put Northern Ireland in control of their latest qualifier at Windsor Park.
The Faroe Islands spurned a chance to halve their deficit when Frodi Benjaminsen's penalty was superbly saved by Roy Carroll.
Finland and Romania now sit two points adrift of Northern Ireland following 1-1 draws with Greece and Hungary respectively.
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