Cardiff burst into life midway through the first half, winger Will Jones made an incisive break into the Swansea 22 and Rhys Howells kept the move alive before lock Nicholas Huntley barged his way through from close range.
Less than five minutes later, they crossed again to take the lead. Captain Jake Cooper Woolley bulldozed his way toward the line but was held just short and, before Swansea's defence had time to regroup, flanker Arthur Ellis picked up at the base of the ruck to dive over.
Cameron Pimlow converted and, when the Cardiff fly-half next had the ball in his hands, he slotted a drop-goal to give his side a 15-6 advantage at the break.
Pimlow struck his second drop-goal soon after the restart, and Cardiff extended their lead just moments later.
Cooper Woolley again set off on a barnstorming run, and this time he went all the way to the try line to give his side a comfortable cushion at 23-6.
Jackson Szabo scored Swansea's only try to give them hope, but any such aspirations were dashed as two late Cardiff tries from lock Craig Lodge and wing Howells sealed a comprehensive victory.
Tries: N Huntley, A Ellis, J Cooper Woolley, C Lodge, R Howells
Con: C Pimlow
Drop-goals: C Pimlow (2)
Try: J Szabo
Con: A Lewis
Pens: A Lewis (2)