Ruud Van Nistelrooy scored a hat trick as the Netherlands overwhelmed Scotland 6-0, and Spain cruised into the finals with a 3-0 victory at Norway.
Croatia also made it to Portugal by winning 1-0 at neighbor Slovenia.
The big surprise was in Istanbul.
Turkey needed just 20 minutes to wipe out Latvia's 1-0 first leg advantage when Ilhan Mansiz hit the target in the 20th minute.
When veteran striker Hakan Sukur made it 2-0 on the night in the 64th minute, it looked as if the Turks were going to the finals.
But Latvia, runner-up to Sweden in Group 4, hit back with goals by Juris Laizans (66th minute) and Maris Verpakovskis (77th) for a tie that stunned the Turks in front of their own fans.
The Dutch went to the Amsterdam Arena trailing Scotland 1-0 and facing the possibility of missing out on Euro 2004, as well as the last World Cup.
But Wesley Sneijder started a feast of scoring with the first after 13 minutes before his free kicks set up the next two.
Van Nistelrooy, back in the starting lineup after a fallout with the coaching staff, helped himself to three, while Frank de Boer and Andre Ooijer also hit the back of the Scottish net to the dismay of former German coach Berti Vogts.
Despite holding a 2-1 first-leg lead over the Norwegians in Oslo, Spain faced the embarrassment of not making it to the finals at neighbor Portugal.
But strikes by Raul Gonzalez, Rodrigues Vicente and Joseba Etxeberria by the 56th minute put the Spaniards well out of reach of the Norwegians, and the visitors were celebrating long before the end.
The lopsided loss means that Norway coach Nils Johan Semb has failed to get the team to the Euros, as well as missing out on the World Cup. Scandinavian neighbors Sweden and Denmark made it to both.
Croatia gained a 1-0 victory at Slovenia to advance to the finals 2-1 on aggregate, having been held 1-1 at home in the first leg.
Two minutes after Juventus defender Igor Tudor had been ejected for a second yellow card in Ljubljana, 10-man Croatia went ahead through AS Monaco's Dado Prso.
The victory meant it gained its second appearance in the finals and maintained an unbeaten record in eight matches against its neighbor.
Croatia reached the quarterfinal at Euro '96 in England and then went on to finish third at the 1998 World Cup in France.
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