A breakaway try from wing Francisco Leonelli means Edinburgh are equal on points at the top of the Celtic League.
Blues (3) 9
Pens: L Thomas (3)
Edinburgh (6) 13
DG: R Lawson
Lee Thomas had booted the Blues into a 9-6 lead at Cardiff Arms Park and with Alasdair Dickinson sin-binned they went seeking a match-winning try.
But they lost the ball deep in their 22, allowing Leonelli's 85m score.
The home side left the field to ringing boos, increasing the pressure on under- fire coach Dai Young and his squad following the European exit last week.
Woeful defeats to Perpignan and Leeds led to widespread reports that Young had offered to resign midweek, although the coach has since denied this.
Criticism from fans has been vociferous and the latest defeat is unlikely to assuage their anger.
The Blues had opened aggressively against the Gunners, but their decision-making was frantic and mistakes rife.
Patient Edinburgh calmly eased ahead with a Duncan Hodge penalty and a drop goal from man-of-the-match Rory Lawson.
Thomas finally got the Blues on the board with a 25th-minute penalty, but that was their only score of a desperate first half.
The home side stepped up the pressure after the break and, although they struggled to find inspiration, they won repeated penalties.
Thomas kicked the Cardiff side ahead and after Edinburgh's fifth successive ruck offence tight-head prop Dickinson was sin-binned.
The Blues went seeking the try, but lost the ball with a botched back move deep in the Scottish side's 22.
Nic De Luca hacked on, the ball bounced fortunately into the full-back's hands, and he fed the supporting Argentinine international Leonelli for a length-of-the-field try.
Hodge added the conversion, and the Blues could find nothing to threaten the visitors in the closing 20 minutes.
Blues coach Dai Young:
"We could have won but there was a breakaway try and a few decisions against us - when you're down you're down.
"It's been a hard week and we were never going to see magic rugby - it was nip-and-tuck but Edinburgh won the kicking game.
"We have to keep working, some of the youngsters put their hands up and showed some pride, something we didn't see at Leeds."
Edinburgh coach Todd Blackadder:
"I have never been more proud of a team, it really was a gutsy performance.
"It was an outstanding display all round but Rory Lawson was a deserved man-of-the-match and an excellent captain.
"[Debutants] Dave Duley was outstanding and Nick De Luca had a very sound game at full-back.
"It takes us a step closer to the title. We've got real belief in the squad and our strength in depth was a key factor tonight.
"There is a long way to go but we'll take this win."
Blues: Macleod; Czekaj, J Robinson, Hewitt, Lomu; L Thomas, R Powell; Yapp, Goodfield, Jenkins; Quinnell, Goode; Molitika, Sowden-Taylor, Rush
Replacements: Stcherbina for J Robinson (74), M Phillips for R Powell (59), B Evans for Jenkins (75), B Davies for Quinnell (79). Not Used: Morgan, Johnson, Lewis.
Edinburgh: De Luca; Leonelli, Godman, Dey Webster; Hodge, Lawson; Jacobsen, Kelly, Dickinson; Strokosch, Duley; Mustchin, Cross, Callam.
Replacements: Smith for Jacobsen (70), MacDonald for Cross (70). Not Used: Traynor, Rennie, Monro, Jorgensen, Pyke.
Referee: George Clancy (Ireland)