Germany needed just a point against Georgia in Leipzig to guarantee themselves a top-two finish in Group D but Max Kruse's 79th-minute winner ensured Joachim Loew's men progressed as group winners on Sunday.
Thomas Mueller had given Germany the lead shortly after half-time, converting a penalty for his ninth goal in the qualifiers, before it was cancelled out almost immediately by Jaba Kankava.
"We're happy on the whole to have secured qualification but displeased with our last two matches," said Loew, who had seen his team lose 1-0 to Ireland on Thursday.
Robert Lewandowski equalled former Northern Ireland striker David Healy's 13-goal record for a single European Championship qualifying campaign as Poland claimed second place in Group D.
Grzegorz Krychowiak netted a 13th-minute opener for the Poles in Warsaw before Jon Walters levelled from the penalty spot shortly after.
But Lewandowski's 15th goal in his last six matches won it for the home side, consigning the Irish, who saw John O'Shea sent off late on, to November's play-offs.
"We are all disappointed after doing brilliantly against Germany (last time out). We let ourselves down. We had the confidence and expected to win," said Ireland defender Seamus Coleman.
In the group's other game, Steven Fletcher scored a hat-trick as Scotland finished their unsuccessful campaign with a 6-0 mauling of Gibraltar in Portugal.
- Albania make history -
========================
Earlier, Albania qualified for their first major international tournament as they beat Armenia 3-0, while Romania also booked their place at the finals after a 3-0 win in the Faroe Islands.
Defeat at home to Serbia on Thursday had left Albania needing three points in Yerevan to edge ahead of Denmark to claim second place in Group I and they made the most of their second chance.
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