The rout did not enable the Tykes to leapfrog eventual group winners Perpignan at the top of the table but it meant they climbed to 20 points and a try tally of 18 in the pool.
That surpassed the 16 tries scored in Pool Three by Stade Francais, who also finished second on 20 points, but Leinster’s win at Bath denied Leeds a last-eight berth.
Andre Snyman (2), Tom Palmer, Tom Biggs, man-of-the-match Justin Marshall and David Doherty went over for tries for Leeds, while their other five-pointer came from a penalty try.
Cardiff, who finished third in the group, were a shambles for the majority of the encounter, with New Zealand legend Jonah Lomu shackled into anonymity.
The build-up to the match had been overshadowed by the controversial awarding of five group points to Leeds following the cancellation of their clash with Calvisano last week.
The Tykes had refused to play on the Italians’ frozen pitch and had been awarded a bonus-point win, giving them a qualification lifeline.
Cardiff took the decision with dignity but felt it set a dangerous precedent for similar future situations.
: De Marigny, Snyman, Vickerman, Bell, Biggs, Ross, Marshall, Shelley, Bulloch, Kerr, Hooper, Palmer, Morgan, Parks, Thomas.
: Doherty for Snyman (66), Care for Marshall (66), Gerber for Shelley (61), Rawlinson for Bulloch (61), Hyde for Palmer (66), Dunbar for Thomas (61).
: R. Williams, Czekaj, J. Robinson, Stcherbina, Lomu, Macleod, M. Phillips, Jenkins, R. Thomas, M. Jones, D. Jones, Sidoli, A. Powell, M. Williams, Rush.
: R. Powell for M. Phillips (68), Goodfield for R. Thomas (73). Not Used: Yapp, Quinnell, Sowden-Taylor, L. Thomas, Davies. Sin Bin: M. Phillips (54).
: C Berdos (France).