Tim Visser's first-half try and a 14-point kicking haul from Greig Laidlaw earned Edinburgh a third win from four European matches to put them in with a chance of a first quarter-final appearance in eight years.
The January fixtures at home to London Irish and against Racing Metro in Paris will decide Edinburgh's fate following a comfortable success, albeit without scoring a second-half point.
Dan Parks kicked three penalties for the Blues, who clinched a losing bonus point which could prove crucial when Leigh Halfpenny booted a 79th-minute penalty.
The Blues fielded five of Wales' World Cup stars and opted to make Gavin Henson continue to wait for his debut, but their back line, in particular, failed to flourish as they suffered their first loss in the competition.
Much of Edinburgh's good play came through Laidlaw, who gave Scotland head coach Andy Robinson food for thought up against international colleague Parks, who may yet miss out on a place in the RBS 6 Nations squad.
Edinburgh's last Heineken Cup contest at Murrayfield was the 48-47 win over Racing Metro and they were the more enterprising and expansive as they sought to avenge last week's 25-8 loss in Cardiff.
The Blues trailed 6-0 after 11 minutes following two Laidlaw penalties before the Edinburgh captain sparked the move which led to the opening try.
Laidlaw found Nick De Luca with a short pass and the centre advanced into the Cardiff 22 before feeding Visser to crash over in the right corner. Laidlaw converted.
After Parks responded with the Blues' first points following an 18th-minute scrum penalty, Laidlaw failed in his fly-half duties for the first time with a missed penalty.
Edinburgh continued to pressure the visitors' line and Visser came close to a second try when fielding Laidlaw's cross-field kick to the left, but the wing was stopped by an illegal tackle from Casey Laulala.
Advantage was played and the move was repeated from left to right this time, but Visser failed to catch Laidlaw's kick with the try line at his mercy.
Edinburgh were then repeatedly repelled by the Blues defence and Laidlaw dropped a goal from close range to keep the scoreboard ticking over.
Parks, perhaps shaken by Laidlaw's contribution, kicked a poor restart and Edinburgh were able to advance into opposition territory once more. And Cardiff's indiscipline was then punished by Laidlaw again following an offside as the hosts took a 16-point half-time lead.
It was deserved, but it could have been more.
Laidlaw missed the chance to kick Edinburgh further ahead after Xavier Rush transgressed at the breakdown before the Blues applied pressure.
Parks spurned a shot at goal to kick to the corner after 53 minutes but Cardiff were held up after driving over from the resulting line-out.
Edinburgh earned a reprieve after first Halfpenny dropped a simple pass with Gavin Evans unopposed outside him and then prop Taufaao Filise allowed the ball to slip out of his grasp while his team-mates were queuing up to score.
The hosts hacked forward, but conceded a penalty and Parks reduced the deficit after 59 minutes.
Parks' half-break and pass almost sent Bradley Davies over on the right, but the lock lost his footing.
Cardiff won a penalty, though, and Parks slotted his third kick to leave the Blues 10 points adrift with 10 minutes remaining.
Halfpenny kicked the Blues' fourth penalty to reduce the deficit to seven as the visitors settled for a losing bonus point.
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