The Chester Road men survived an early scare, when the visitors snatched a goal after just four minutes of the first period.
Deeside had to wait until the 36th minute to equalise, as Hull threatened to turn the Laidler Conference form book on its head. And a Dragons rally late in the third period sealed the points against a determined Jets outfit.
Paul said: “It was really close tonight and I think the way our team plays is governed by the way we start games. We began slowly against a team with young kids in cages, trying to prove themselves.
“The effort they put in stunned us a little bit and credit to Hull, they put an awful lot of effort in. We got the puck up as fast as we could and eventually triumphed.
“We look at it as every game is a final for us. Other teams are bringing their A game, so we won’t get any easy matches. They’re coming out firing on all cylinders, so I’m proud of the lads tonight.”
That early Hull strike was cancelled out by Filip Supa on 36 minutes, before the Jets regained the lead with just eight minutes of the game remaining.
An immediate reply from Marc Lovell pulled Deeside back level on 55 minutes, ahead of further goals from Supa and Alex Parry.
Paul added: “The result is always more important than the performance and I’ve said before that sometimes we have to win ugly.
“It’s no good playing well and putting in 50 shots if you then lose 5-0. Tonight we faced a very determined Hull side and the history books will show that we won.”