The Airlie Birds looked more physically powerful and much quicker and sharper than the home side.
Theo Fages was to the fore as Saints made a strong start to the game, the French half back’s kicking game was precise and pressurising.
The visitors fought back though, with their pack driving forwards and laying a platform for their impressive halves.
Hull went into the interval 25-12 in front, a fair reflection of the way their forwards had chewed up metres. Marc Sneyd dropped a goal in the last minute of the half, capping a fine performance from the scrum half.
Momentum shifted in the second half, after Luke Walsh bagged an early try for the home side.
But Hull did not let it shift too far, and hit back to lead 31-18 with less than 20 minutes to play, and Saints looking tired.
“I thought it was a massive effort from our forwards in this heat,” man of the match Marc Sneyd told BBC Sport.
“We defended outstandingly – everyone did, one to 17. I think we deserved it.
“I think they [Saints] were little bit off defensively today, but we’ve turned up with the right attitude and done what we need to do.
“We’re in the next round now. Winning the Challenge Cup would be a massive thing.”