The full-back kicked both conversions as well as five penalties, while Edinburgh's points all came from the boot of captain Greig Laidlaw, who marked his first appearance of the season with four penalties.
Halfpenny was presented with an early chance to get his kicking range with a penalty on the left wing on four minutes, with the Welsh international duly obliging to hand his side a 3-0 lead.
But he failed to split the posts again five minutes later as a penalty in front of the posts, albeit from distance, flew wide of the uprights.
Edinburgh were level on the quarter hour mark when the Blues were penalised for tackling in the ruck and Laidlaw, back to full fitness following his knee injury, added the points.
Laidlaw again made his presence felt on 23 minutes with another penalty that edged Edinburgh into the lead.
But the lead proved to be shortlived as Halfpenny slotted over his second penalty from the touchline just minutes later after Edinburgh were stung for not rolling away.
Edinburgh lost Ben Atiga to a dislocated finger on 26 minutes, with the centre replaced by Matt Scott, and it went from bad to worse shortly afterwards as they conceded the first try of the afternoon.
A maurauding counter attacking run by Blues' Harry Robinson played in Williams, and although he was held up on the 22, the ball was recycled out wide for Cuthbert to sneak over in the corner, despite the best efforts of Harry Leonard.
Halfpenny again added the extras as the home side got themselves 13-6 up just short of the half hour.
But with ten minutes of the half remaining, Laidlow slotted a third penalty after Sam Warburton was penalised before the break, leaving the Edinburgh fly-half to continue his 100 per cent kicking record and reduce the arrears to a single point.
He was however to make his first miss of the afternoon after the break when his 43rd-minute penalty died in the wind, knocking the left post and bouncing back into play.
But his side were quickly on the attack again, as a series of phases saw Edinburgh camped just short of their opponents line, before Tomas Lionardi, on his debut, looked to have placed the ball over the line from within the ruck.
However after consultation with the television match official, the try was wiped off with the Argentinean instead penalised for not immediately placing the ball after being tackled, leaving the scores at 13-12 on 45 minutes.
The Blues managed to get their first points of the second half on the board in the 53rd minute, with the kick again coming from the boot of Halfpenny who slotted over his third penalty before adding another shortly afterwards.
The full-back was having an impressive afternoon, and he fed Cuthbert to charge at the Edinburgh defence as the Blues looked to extend their lead further on 59 minutes.
The move was eventually held up ten metres short of the try line, but referee George Clancy took play back for an earlier penalty, handing a yellow card to Cornell Du Preez for continual team infringement, leaving Halfpenny to add three more for 29-12.
Cardiff added a second try on 67 minutes as a flowing counter attack saw the ball moved up the pitch with pace before Halfpenny offloaded to Warburton, who duly fed Cuthbert for his second try of the match.
Cuthbert had a chance to round off his afternoon with another try late on, but Edinburgh's Harry Leonard and Jack Cuthbert combined to hold the wing up on the line, but Cardiff Blues side had done enough for victory.
|Cardiff Blues Score Card|
|Edinburgh Rugby Score Card|