Robbie Keane scored a 12-minute hat-trick as Republic of Ireland demolished Gibraltar 7-0, while an Akaki Khubutia own goal handed Scotland a 1-0 triumph over Georgia in EURO 2016 qualifiers.
Arkadiusz Milik and Sebastian Mila found the net as Poland stunned Germany with a 2-0 victory.
Joachim Low's world champion, which had laboured to a narrow 2-1 win over Scotland in its Group D opener, was below par and allowed Poland to clinch the points as it fell to a first competitive defeat in 19 outings.
Albania missed out on the chance to go top of Group I as it was held to a 1-1 home draw by Denmark.
Gianni De Biasi's men claimed a shock 1-0 triumph in Portugal to get its campaign under way last month and looked set to to make it two wins from two.
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 it drew 1-1 in Armenia.
Northern Ireland sits atop Group F at the end of matchday two, having beaten Faroe Islands 2-0 in Belfast to seal its 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 its latest qualifier at Windsor Park.
Faroe Islands spurned a chance to halve the deficit when Frodi Benjaminsen's penalty was superbly saved by Roy Carroll.
Finland and Romania now sit two points adrift of Northern Ireland after 1-1 draws with Greece and Hungary respectively.