The Red Dragons started the game magnificently and were ahead after just three minutes courtesy of David Brooks, and the hosts doubled their lead later in the first half thanks to a stunner from Neco Williams.
Marksman Teemu Pukki brought Finland back into contention for progression with a strike just prior to the half-time whistle, however a relatively-comfortable second period saw further Welsh goals via Brennan Johnson and substitute Daniel James.
Following a solid performance and win over Markku Kanerva's men in the Welsh capital, the only team that now stands in the way of Rob Page's troops and the Euros is Poland, who thrashed Estonia 5-1 in the other semi-final in Warsaw.
Looking to reach a major tournament for the first time since the retirement of legend Gareth Bale, Johnson was handed the responsibility of leading the Welsh line in Cardiff, with Ipswich Town loanee Kieffer Moore settling for a place amongst the substitutes.
Daniel Hakans represented a new face in the Finland attack but a close-knit partnership of Pukki and Joel Pohjanpalo persists from the nation's most-recent and only appearance at a major tournament, with the pair playing a massive part for their country at the delayed Euro 2020.
With Wales needing to win back-to-back games at the Cardiff City Stadium in the space of five days to book their place in Germany in June, Page's side wasted little time in hitting the front in this semi-final contest, with a returning star providing the decisive touch.
Starting the move on the left, Harry Wilson and Johnson played a neat interchange which allowed the Fulham winger to unleash a stinging shot onto the goal of Lukas Hradecky, and the Bayer Leverkusen stopper could only parry the ball into the path of Brooks, who controlled his volley into the net.
Despite a brilliant beginning on the scoreboard for the Red Dragons, the visitors were enjoying periods of possession and could have equalised when Pukki's clever movement allowed him a run on goal, although the veteran's effort was straight into the thankful arms of Danny Ward.
Wales managed to double their advantage in sensational fashion when Wilson faked to shoot from a free kick and laid the ball off brilliantly for Neco Williams, who punched a curling strike into the top corner, past the outstretched and helpless Hradecky.
It looked as if the hosts would be taking a two-goal advantage into half-time interval but Finland's all-time record goalscorer was not following the Welsh script, with Pukki racing through on goal, getting across the challenge of Chris Mepham and slotting cooly past Ward into the near post.
After a portion of sluggish defending which allowed Kanerva's men back into the game, Wales were quick to restore their two-goal buffer during the opening stages of the second period, when Page's troops once again took advantage of a set-piece situation to inflict damage on the visitors.
Following a delivery from the left foot of Ben Davies, Joe Rodon rose to win the first ball which bounded towards Brooks, who scuffed his effort into the path of the onrushing Johnson, with the former Nottingham Forest youngster having the simplest of jobs to tap home from close range.
With Finland needing to find a way back into the match to keep their Euro 2024 hopes alive, there was plenty of space to attack for the likes of Johnson, James and Wilson, with the latter sending a curling shot just wide of Hradecky's goal when the winger had passing options to his left and right.
Wales thought they had netted their fourth of the evening in the 79th minute when Tottenham Hotspur's Davies powered a header in off the post and past the attentions of the Finnish defence, however a VAR check revealed that Rodon had blocked off Hradecky as he attempted to claim the ball.
The Red Dragons were not made the wait much longer for that fourth goal, though, with a lapse in concentration from Miro Tenho allowing James to rob possession and race through on goal, and the ex-Manchester United winger calmy rounded the keeper and converted into an empty net.
Following a highly-convincing win over Finland, all those of a Welsh persuasion will now quickly turn their attentions towards a monumental meeting with Robert Lewandowski and Poland on Tuesday, when the winner of the clash will earn the right to join the tricky-looking Group D of Euro 2024.