The result leaves the Blues level on points with Edinburgh at the top of Pool 2 with two rounds of action to play in January.
Greig Laidlaw kicked the hosts into an early lead with two early penalties before wing Tim Visser crossed for the game’s first try after 14minutes.
Laidlaw added the extras with the boot from the touchline to kick Edinburgh into a 13-0 lead after 15minutes.
Dan Parks then got the Blues off the mark with a penalty but six more points from the boot of Laidlaw stretched Edinburgh’s advantage going into the break.
Parks scored the first points of the second period to cut the deficit after 60minutes and then kicked his third penalty of the evening.
With a minute remaining Wales star Leigh Halfpenny kicked a long-range penalty to secure the losing bonus point.
