London: Scotland gave up a 90th-minute equalizer before winning a tense penalty shootout to reach its first major tournament in 22 years.
Hungary found two late goals to beat Iceland 2-1. Slovakia also lost its lead late but scored an extra-time winner.
North Macedonia had a smoother ride through the European Championship playoffs on Thursday and will make its major tournament debut next year.
The 24-team lineup was completed for the pandemic-delayed Euro 2020 with four playoffs that served up plenty of late-game drama in almost entirely empty stadiums.
The biggest winners were Hungary and Scotland who are among the 12 host nations scattered across Europe and now get two home games in the group stage next June.
Scotland converted all five penalties in the shootout after a 1-1 draw against Serbia, before goalkeeper David Marshall saved the home team's final spot kick from Aleksandar Mitrovic.
The Scots reached their first tournament since the 1998 World Cup and will have two games in Glasgow against Croatia and the Czech Republic along with a trip to face old rival England at Wembley Stadium.
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Hungary trailed against Iceland from the 11th minute until leveling in the 88th, and when extra time looked likely Dominik Szoboszlai rifled in a low shot to seal the stunning victory in stoppage time in Budapest.