Edinburgh reclaimed their position at the summit of Pool 2 after overcoming Cardiff Blues 19-12 in the Heineken Cup at Murrayfield on Friday.
But a late Leigh Halfpenny penalty secured a potentially crucial bonus-point for the Blues.
Two penalties from fly-half Greg Laidlaw and the only try of the game from Tim Visser established an early 13-0 lead for the hosts.
Dan Parks responded with three penalties but Laidlaw added two further three-pointers, before Halfpenny came to the visitors rescue.
To stand a chance of qualifying, the Scottish outfit had to defeat the Cardiff Blues, and they set the tone early on.
The homing boot of Laidlaw kicked the hosts into an early lead before he added another after eleven minutes.
Edinburgh continued to dominate and it was no surprise to see Visser scamper in at the corner with the score being confirmed by the Television Match Official.
Their scrum-half converted superbly from out wide, but Parks managed to get Cardiff on the scoreboard with a penalty.
However, a drop-goal and another three-pointer late in the half gave them a deserving 19-3 advantage at the break.
It was the Blues who lifted their intensity in the early stages of the second half but they were met with excellent Edinburgh defence. Taufa'ao Filise was held up over the line, but they were finally rewarded when Parks kicked successive penalties to bring the Welsh region back into match with ten minutes to go.
And it was left to Halfpenny to convert a 45-metre penalty and steal a losing bonus-point for the visitors, who drop to second because of tries scored.
Pens: Laidlaw 3
Pens: Parks 3, Halfpenny
Edinburgh: 15 Chris Paterson, 14 Lee Jones, 13 Nick De Luca, 12 James King, 11 Tim Visser, 10 Greig Laidlaw (capt), 9 Mike Blair, 8 Netani Talei, 7 Roddy Grant, 6 David Denton, 5 Sean Cox, 4 Grant Gilchrist, 3 Geoff Cross, 2 Ross Ford, 1 Allan Jacobsen.
Replacements: 16 Steven Lawrie, 17 Kyle Traynor, 18 Jack Gilding, 19 Esteban Lozada, 20 Ross Rennie, 21 Phil Godman, 22 Matt Scott, 23 Tom Brown.
Cardiff Blues: 15 Leigh Halfpenny, 14 Gavin Evans, 13 Casey Laulala, 12 Jamie Roberts, 11 Chris Czekaj, 10 Dan Parks, 9 Lloyd Williams, 8 Xavier Rush, 7 Sam Warburton, 6 Michael Paterson, 5 Paul Tito, 4 Bradley Davies, 3 Tau Filise, 2 T Rhys Thomas, 1 Gethin Jenkins.
Replacements: 16 Ryan Tyrrell, 17 John Yapp, 18 Scott Andrews, 19 Josh Navidi, 20 Maama Molitika, 21 Richie Rees, 22 Ceri Sweeney, 23 Dafydd Hewitt.
Referee: Pascal Gauzere