Albania shocked Portugal, world champions Germany denied battling Scotland and minnows Gibraltar were demolished by Poland in the opening games of Euro 2016 qualifying.
Portugal, who were missing Real Madrid's Cristiano Ronaldo, lost 1-0 at home to a team ranked 71st in the world.
Slavia Prague forward Bekim Balaj struck the killer blow early in the second half, with the home crowd booing their team at the end of the game.
Georgia 1-2 Ireland
Germany 2-1 Scotland
Gibraltar 0-7 Poland
Hungary 1-2 Northern Ireland
Faroe Islands 1-3 Finland
Greece 0-1 Romania
Denmark 2-1 Armenia
Portugal 0-1 Albania
"It's a really bad result," said Portugal striker Nani. "We've started qualifyng badly, now we have to pick ourselves up. We have to improve."
Minnows Gibraltar were given a lesson on their introduction to competitive internationals as a UEFA member by Poland as Bayern Munich's Robert Lewandowski scored four times in a 7-0 romp.
In Dortmund, Germany got their qualifying campaign up and running with a 2-1 win against a spirited Scotland.
A goal in each half from Bayern Munich attacker Thomas Muller ensured they won their first competitive fixture since the World Cup.
Scotland were rewarded for a positive second-half approach when winger Ikechi Anya raced clear to equalise on 66 minutes.
But the visitors failed to clear a corner four minutes later and Muller capitalised to thump home his 24th international goal.
Germany are now undefeated in 33 World Cup and European Championship qualifying games.
German manager Joachim Low said: "In the first half we had complete control of the game. We lost control a little bit in the second half. Scotland scored but we reacted well."
Meanwhile, Everton winger Aiden McGeady bagged both goals for Ireland as his side beat Georgia 2-1 in Tbilisi, curling his second in the 90th to secure all three points.