Before the game both sides came together for an impeccably observed minute's silence in memory of Wales and British Lion Dr Jack Matthews who passed away in July.
Edinburgh took the lead in only the third minute as Cardiff were penalised at a scrum - Laidlaw doing the honours to open the scoring.
Having weathered an early Edinburgh storm, Cardiff began to establish some possession and territory and after a series of attacks in the visitors' 22, they earned a penalty in front of the posts.
A kicker like Halfpenny was never likely to miss and the Welsh international made no mistake to draw the sides level.
Virtually from the kick-off Edinburgh responded - inevitably through winger Tim Visser after some fantastic work from second row Sean Cox.
The lock showed great awareness to use the dummy run of David Denton and ghost through a gap before passing around the tackler for Visser to sprint over in the corner - despite the best efforts of Halfpenny.
Laidlaw missed the conversion and was off-target again a couple of minutes later after the Blues scrum was again put under huge pressure with Tau Filise struggling in the unfamiliar loosehead position.
Cardiff took full advantage of Laidlaw's struggles with the boot as they earned a second penalty ten metres inside the visitors' half and Halfpenny knocked over his second penalty of the night to bring the score back to 8-6.
Having been on the back foot for much of the half, the Blues showed their clinical side earning a third penalty as Stuart McInally was harshly adjudged to be handling the ball off his feet.
Halfpenny needed no second invitation and slotted the kick to make it 9-8 to the Blues at half-time.
After the break Edinburgh again got themselves into good position but, after a turnover from the Blues, Tom James went on a searing run, but having stretched the Edinburgh defence he failed to look around him and the move broke down.
James was a constant thorn in the Edinburgh side and another break led to the ball being spread wide and with a try looking certain, an illegal turnover from Greig Tonks earned the full-back ten minutes in the sin bin.
With a man down Edinburgh were struggling to cope with the barrage of Cardiff attacks and it was the Blues' own giant winger Alex Cuthbert who crashed through the weak tackle of John Houston to score the home side's first try - Halfpenny converted from right in front to make it 16-8.
Edinburgh needed an immediate response and they got it with a penalty at a breakdown as Laidlaw found his range to bring the visitors back to within five.
Halfpenny added another penalty but the Blues were soon reduced to 14 men themselves when blindside Josh Navidi was sent to the bin.
Edinburgh took advantage of a dropped ball in midfield to hack forward and after wing Lee Jones was stopped short, Navidi couldn't help himself and turned the ball over illegally.
From the ensuing penalty Edinburgh took the scrum and their decision was vindicated as the Cardiff set-piece disintegrated, leaving referee David Wilkinson with little option but to give the penalty try, Laidlaw's conversion brought Edinburgh back to within a point.
And with two minutes remaining Edinburgh attacked again and when Laidlaw got his chance, his drop goal went straight through the sticks to deny the home side.
|Cardiff Blues Score Card|
|Edinburgh Rugby Score Card|