Tom Brown did threaten an Edinburgh comeback as he grabbed the home side's second try of the game, but it wasn't to be as Hewitt went over with five minutes remaining to secure a RaboDirect PRO12 double for Cardiff over their Scottish opponents.
However it wasn't all doom and gloom for Edinburgh as Cornell du Preez went over at the death to earn his side a losing bonus point.
After just two minutes Cardiff Blues found themselves ahead as Gareth Davies slotted a penalty, although Edinburgh were level moments later as Jack Cuthbert replied with a three-pointer of his own following a high tackle.
Cardiff threatened to score the game's first try on seven minutes but a testing grubber kick ran out of play, and the visitors soon found themselves behind as Scott did indeed grab the evening's first score.
The Scotland centre showed great pace and strength, bursting on to the ball before fending off a defender to race in under the posts, Cuthbert adding the easy conversion.
Another grubber kick nearly came off for Cardiff on 14 minutes only for a knock on to spoil the move, but they did have a try shortly afterwards as Allen touched down, Davies levelling the scores from the tee.
And after half an hour Cardiff were back in front as lock Paulo battered his way over, Davies adding the extras from the touchline.
The Blues maintained their seven-point lead up until half-time and things went from good to great for the visitors one minute after the restart as Fish scored, Davies again converting.
This woke the hosts up and on 47 minutes they halved the deficit as Cuthbert was successful with the touchline conversion after Brown had dotted down in the corner after a pick and snipe.
Some great offloading rugby saw Edinburgh back into Cardiff's 22 shortly afterwards but the period of pressure came to an end with a knock on.
On 65 minutes it was the visitors turn to go close and the Blues were only kept out by some last-gasp Edinburgh defending.
Alex Cuthbert looked like making the game safe for Cardiff Blues late on after breaking through, only to knock on after a great tackle by Edinburgh namesake Jack.
But the visitors did put the game to bed with five minutes remaining as Hewitt scored out wide, wrapping up a bonus point in the process.
Davies missed the conversion and Edinburgh made the most of it, helping themselves to a losing bonus point as du Preez went over at the death, Jack Cuthbert's touchline conversion hitting the post.
|Edinburgh Rugby Score Card|
|Cornell du Preez||1||5|
|Cardiff Blues Score Card|