Rob Page's side stormed into a two-goal lead thanks to strikes from David Brooks and Neco Williams in Cardiff. Teemu Pukki reduced the deficit just before the break, but Brennan Johnson and Daniel James netted in the second half to keep Wales' Euro dreams alive.
Bidding to reach a third consecutive European Championship, Wales will take on Poland in the play-off final at the Cardiff City Stadium on Tuesday. Poland were 5-1 winners against Estonia in their semi-final on Thursday.
"We got off to the best possible start. Everyone put in a performance. It could have been five or six in the end, but the message is that this is half-time," Page said. "We're going to enjoy the win and take this into the final. We've now got a massive effort to go. We can't wait. Roll on Tuesday."
Finland boss Markku Kanerva added: "I'm disappointed. We had disastrous starts to both halves. We didn't reach the level I wanted." After failing to qualify for a major competition for over 50 years following their appearance at the 1958 World Cup, Wales are one win away from making it to a fourth tournament in their last five attempts.
In their first qualifying campaign since the retirement of Gareth Bale, Wales are proving they can cope without the former Real Madrid and Tottenham star. The 2016 European Championship semi-finalists look battle-tested in the race to reach the finals in Germany after previously surviving play-off pressure to reach the 2022 World Cup.
With the atmosphere already deafening prior to kick-off, Brooks raised the decibel levels even louder in the third minute. Page's team tore through the Finland defence as Harry Wilson found space for a low shot that Finland keeper Lukas Hradecky could only parry to Brooks, who kept his
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