Scotland international Gregor Townsend was a Borders sinner as Cardiff emerged from the Mansfield Park battle having broken their Celtic League duck.
Borders triumphed in the try count but were made to pay for a spate of missed goal kicks, as Cardiff stand-off Iestyn Harris snuffed them out with six penalties in Pool B.
Kevin Utterson edged the Scots in front with a kick after just two minutes on Friday.
But the Welsh side wasted no time in replying, Harris bagging an identical score when the Borders back line crept offside.
Harris landed two more before the break, while Utterson and Gregor Townsend were off target three times between them.
Borders restarted in hungry fashion and claimed a superb try through wing Nikki Walker.
He launched the move then finished in style after a scrum and fine link work involving skipper Gary Armstrong and back-row Andy Rennick.
Townsend converted to edge them back in front, but Harris was quick to reply with another penalty to set up a dramatic finale.
Borders created a superb second try by Scott Paterson after a long-distance move that featured a patient series of phases.
But Townsend shook his head in disgust as he sent the conversion wide from dead in front of the posts.
To compound his frustrations, Harris quickly took his penalty tally to a decisive half dozen to help his team break their Celtic League duck in far from convincing style.
Borders (3) 15: Tries: Paterson, N. Walker. Con: Townsend. Pen: Utterson.
Cardiff (9) 18: Pens: Harris 6.
Att: 4,000.
Borders: S Paterson; N Walker, S Cranston, K Utterson, C Moir; G Townsend, G Armstrong (capt); P Thomson, S Scott, B Douglas, D Weir, R Metcalfe, A Rennick, M Taylor, S Sititi.
Reps: J Stuart, C Laidlaw, I Fairely, C Feather, C Stewart, C Dunlea, S Gunn.
Cardiff: R Williams; Morgan, J Robinson, P Muller, A Sullivan; I Harris, R Powell; T Payne, G Woods, Fourie, A Jones, Tait, R Appleyard, M Williams (capt), D Baugh.
Reps: G Powell, A Lewis, L Tait, D McShane, R Smith, N Robinson, N Walne.