The Poles hammered lacklustre Estonia 5-1 after the visitors were left with 10 men before the half-hour mark.
In Cardiff, a leaping David Brooks got the hosts off to a dream start in the third minute when Harry Wilson's shot was saved and rebounded to him for the knock-in.
Neco Williams made it 2-0 in the 38th when he blasted the ball into the top corner off a backheeled free kick by Wilson on the edge of the box, but Finland pulled one back with Teemu Pukki's 40th international goal on the stroke of half-time.
Brennan Johnson restored the two-goal cushion from close-range in the 47th, after Ethan Ampadu headed on from a free kick, and stand-in captain Ben Davies had a fourth ruled out by VAR in the 79th.
James then made it 4-1 in the 86th when he sprinted clear, dribbled around goalkeeper Lukas Hradecky and slotted the ball into an open goal.
Wales will now play Poland at the same Cardiff stadium on Tuesday.
Poland overwhelmed powerless Estonia who rarely left their own half and had no goal attempt until midfielder Martin Vetkal pulled back a consolation goal in the 78th minute.
Przemyslaw Frankowski put Poland ahead in the 22nd minute, when he received an elegant pass from Jakub Piotrowski to score with a low finish, and Piotr Zielinski doubled the lead after the break, nodding home a cross from Nicola Zalewski.
Piotrowski made it 3-0 with a shot from a distance in the 70th minute, three minutes before Estonia defender Karol Mets gifted Poland their fourth with an own goal, and Sebastian Szymanski bundled in the fifth from close range.
Estonia went down to 10 men in the 27th minute when defender Maksim Paskotsi saw his second yellow card for a challenge on Zalewski.
Greece, Georgia, Ukraine and Iceland also prevailed.
Ukraine scored twice late on to come back and beat Bosnia-Herzegovina 2-1 away in a famous victory for the war-torn nation. Roman Yaremchuk and Artem Dovbyk netted on 85 an 88 minutes after Mykola Matviyenko's own goal.
Georgia will host 2004 champions Greece, who beat Kazakhstan 5-0 in their play-off semi-final, in the Path C final on Tuesday and victory will hand them one of the three remaining places at the Euros in Germany from June 14 to July 14.
Greece struck twice early through captain Anastasios Bakasetas and  Dimitrios Pelkas, with further goals from Fotis Ioannidis, Dimitrios Kourbelis and Alexandr Marochkin (own goal).
The Georgians have played for the Soviet Union in major tournaments but never for their independent nation.
Karlsruhe's Budu Zivzivadze hit the post early on in the Tbilisi rain and then broke the deadlock for the dominant hosts on 40 minutes.
The visitors thought they had levelled through Gerson Rodrigues early in the second half but a VAR check meant play was brought back and Maxime Chanot was sent off for a professional foul moments earlier.
Zivzivadze then struck again soon afterwards.
In Path B, Iceland won 4-1 against Israel courtesy of a hat-trick by Genoa's Albert Gudmundsson in a game played in Budapest due to the Gaza war.
The Icelanders will face Ukraine in Poland's Wroclaw on Tuesday in the decider, with the prize being a place in Group E with Belgium, Slovakia and Romania.
Meanwhile, Portugal swept past Sweden 5-2 in a friendly as manager Roberto Martinez rested Cristiano Ronaldo and several other key players in the build-up to the European Championship in Germany.
Rafael Leao, Matheus Nunes, Bruno Fernandes, substitute Bruma and Goncalo Ramos scored for the Portuguese, who stormed into the Euro 2024 finals by winning all 10 of their qualifiers.
with DPA
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