Paul Thompson's side got stuck in straight away from the face off and were ahead on 2.06 when Carlyle Lewis netted.
Dan Carlson scored a minute later with Russ Cowley making it 3-0 before the the ninth minute.
Dunaujvaros pulled one back through Peter Misal in the 11th minute but 24 seconds after this goal, Corey LeClair went down the other end and delighted the Blaze travelling support with a goal to make it 4-1.
In the second period, Galanisz scored but LeClair added his second of the night after 33.22.
Blaze were not wracking up penalties and were twice down to 3v5 which let Galanisz make the score 5-3 before Barrie Moore hit back in the 46th minute.
Another powerplay goal for the Hungarians further reduced the margin of victory but the Blaze hung on to reach the final against Bolzano.
This game in which the winning team travel to Rouen, starts at 6.30pm Cov time and you can hear the game live on BBC Coventry & Warwickshire.