In-form Fish raced over in only the second minute of the game after a sweeping team move as Cardiff Blues flew out of the traps.
But the rest of the first half was one of frustration for the home side as they played some nice attacking rugby without a killer finish with impressive ball carrying Number Eight Manoa Vosawai twice narrowly denied a score.
The theme continued in the second half with Patchell denied a try by the TMO, but the home side still controlled the late stages to make it four successive league victories.
The very first attack of the game saw Blues go wide at pace and slick hands from Jarrad Hoeata released Aled Summerhill into space and he drew the final man and sent Fish over for a fine try.
Prop Salesi Ma’afu was straight into the action on debut as he impressed in the opening scrums but a penalty against him for not rolling away allowed Edinburgh to kick for territory and look for an immediate response.
A big driving lineout gained yards before more slick hands from Patchell sent Scully away only for the wing to be dragged out.
Vosawai thought he had a second score after 13 minutes, after another powerful lineout drive, but the try was chalked off by the TMO for a double movement as the big Number Eight went for the line under pressure from three men.
Patchell slotted a penalty, after Edinburgh were caught offside, to open up a 10-0 lead after 16 minutes. But six minutes later a penalty from visiting scrum half Nathan Fowles, for the same offence, put Edinburgh on the board.
Blues were playing some incisive attacking rugby as Vosawai, Navidi and Jenkins carried up strong to set the platform for the backs to fire with Fish close to slipping through the defensive net.
A huge driving maul saw Vosawai break off the back, bash through defenders but one last ditch tackle dislodged the ball as he looked to go to ground for the score as a good chance went begging.
Another hurtling run from Vosawai put Cardiff Blues on the front foot but Patchell saw his penalty, after a breakdown penalty infringement, bounce back off the upright as the home side took a 10-3 lead into the dressing rooms.
A tight opening to the second half saw both teams kick for territory with Edinburgh now having the advantage of the wind.
An off the ball tackle from Ma’afu saw a penalty conceded and Edinburgh kicked to the corner only for Cardiff Blues to turnover ball on the floor and Fish to smash a booming clearing kick away.
The Scottish side were looking to dominate territory and slowly turned the screw to try and make the home side pay for missing out on points in the first half. But a yellow card for Rory Sutherland after 55 minutes saw momentum swing back for the hosts.
Patchell missed another kick as Cardiff Blues before he was denied a try by the TMO for a foot in touch to the total dismay of the home crowd.
A tense and fraught final quarter ensued as the home side looked to protect the slender lead. And despite a rally from the visitors in the final minutes it was Cardiff Blues who took the points on offer.
02m Fish t Patchell c 7-0
16m Patchell p 10-0
22m Fowles p 10-3
Cardiff Blues: 15 Dan Fish, 14 Blaine Scully, 13 Rey Lee-Lo, 12 Gavin Evans (J Evans 62), 11 Aled Summerhill, 10 Rhys Patchell, 9 Tavis Knoyle (T Williams 62); 1 Thomas Davies (Thyer 73), 2 Matthew Rees, 3 Salesi Ma’afu (Lewis 48), 4 Jarrod Hoeata (Cook 75), 5 James Down, 6 Ellis Jenkins, 7 Josh Navidi, 8 Manoa Vosawai
Replacements: 16 Ethan Lewis, 17 Bradley Thyer, 18 Dillon Lewis, 19 Macauley Cook, 20 Jevon Groves, 21 Tomos Williams, 22 Jarrod Evans, 23 Elis-Wyn Benham