Cardiff - Gareth Steenson's boot did enough to see Exeter Chiefs past Cardiff Blues at Arms Park with a 19-13 victory.
The Blues will be ruing a missed opportunity to secure a place in the latter stages of Europe's second tier competition as they had their fate in their own hands but they could yet qualify if several results go their way on Sunday.
The visitors, who had just one win in this season's competition prior to kick-off, sprang out of the blocks and into the lead as flanker Don Armand powered his way over from short range inside the opening five minutes and Gareth Steenson added the conversion.
A pair of Steenson penalties extended the advantage even further as the first half wore on and the Chiefs' forwards were getting the better of their opposite numbers by and large in the set piece and in the loose.
Wales and Lions full-back Leigh Halfpenny's boot did make a dent in Exeter's lead just before the half-hour mark though and the hosts were right back in the match at halftime as Alex Cuthbert crossed the whitewash late on.
The winger sprinted over underneath the posts and dotted the ball down to finish off an excellent move that started around the halfway line and make it 13-10 at the interval.
Halfpenny and Steenson exchanged penalties in the early stages of the second half and both sides had opportunities to score a second try as the game broke up and players chanced their arm more and more.
Both defences were in top form though and it was left to the two usually reliable goal-kickers to settle the outcome of the match as it reached its climax.
A yellow card for Exeter scrum-half Dave Lewis with just under 10 minutes remaining tilted the balance in the home side's favour as well but two rare misses from the tee from Halfpenny let the Chiefs off the hook.
The Blues hammered away at the opposition defence for the vast majority of the closing stages but they couldn't find a way through and Exeter got further reward for their defensive efforts in the final minute as Steenson kicked his fourth penalty of the afternoon to secure the win.
BLUES: Try: Cuthbert, Con: Halfpenny, Pens: Halfpenny 2
EXETER: Try: Armand, Con: Steenson, Pens: Steenson 4, Yellow Card: Lewis
HEINEKEN CUP RESULTS:
Cardiff (WAL) 13 Exeter (ENG) 19
Glasgow (SCO) 8 Toulon (FRA) 15
Saracens (ENG) 64 Connacht (IRL) 6
Zebre (ITA) 6 Toulouse (FRA) 16
Leicester (ENG) 19 Ulster (IRL) 22
Montpellier (FRA) 24 Treviso (ITA) 6