Finland qualified for a major championships for the first time in their history as a 3-0 home win over Liechtenstein booked their place at the Euros.
Two goals from Norwich striker Teemu Pukki, the first a penalty, added to Jasse Tuominen's opener and guaranteed the hosts second place in Group J behind Italy.
It ended a run of 32 failed attempts to qualify for either the World Cup or European Championships.
Having finished fifth out of six teams in their qualifying group for the last World Cup, Finland - who also topped their Nations League group last year - beat the likes of Bosnia-Herzegovina and Greece to automatic qualification this time around.
Elsewhere in Group J, Italy made it nine wins from nine at the top of the pool thanks to a 3-0 win away to Bosnia-Herzegovina, Francesco Acerbi, Lorenzo Insigne and Andrea Belotti with the goals, while Greece won 1-0 in Armenia thanks to Dimitris Limnios' goal.
Wales are assured of a place in the Euro 2020 play-offs thanks to Sweden securing automatic qualification from Group F.
The Swedes won 2-0 in Romania thanks to first-half goals from Marcus Berg and Robin Quaison to sew up second spot.
Sweden's win ended Norway's faint hopes of a second-placed finish after they had won 4-0 at home to the Faroe Islands earlier in the evening.
Goals from Tore Reginiussen and Iver Fossum put Norway, who have a guaranteed play-off spot, two up after only eight minutes and a second-half double from Alexander Sorloth sealed a routine win.
Group winners Spain hammered Malta 7-0, with the final five goals coming in the last half-an-hour.
Goals from Alvaro Morata and Santi Cazorla put the hosts two up at the break before they moved through the gears in the second half.
Two became six in the space of 10 second-half minutes thanks to goals from Pau Torres, Pablo Sarabia, Daniel Olmo and Gerard Moreno before Jesus Navas completed the rout.