Danny Wilson’s men had looked set to suffer New Year’s Day heartbreak as a late from Gareth Davies looked set to send Scarlets to the top of the league.
But in a stunning late show it was Wales wing Cuthbert who was the hero he scored two minutes from time to spark wild celebrations in the Welsh capital.
Earlier the home side had fallen behind to tries from Ken Owens and DTH van der Merwe.
But after Cory Allen cut the lead further tries from Dan Fish and Kristian Dacey set up the most thrilling of finishes as Cuthbert took centre stage.
Played out in front of partisan and vocal home crowd, it was Blues who flew out of the traps with a Tom James break down the left wing, after slick quick handling down the line, seeing the crowd on its feet.
And when a penalty was secured in field up stepped Patchell to nudge over the kick for an early lead.
A brilliant touch finder from Patchell set up a five-metre lineout that the home side looked to drive over. But turnover ball saw Gareth Davies break into space and bounce off tackles before a grubber kick in behind just ran dead.
The game’s opening try came from nowhere and was a late Christmas gift from the home side as a lineout went horribly long and a grateful Ken Owens gobbled up the ball and crashed over from close range. Thomas converted for a 7-3 lead.
The forwards drove up close again but spilled ball cost them a chance to strike back before a second gift in five chaotic minutes as an intercept pass from James saw DTH van der Merwe race over from the halfway line to extend the lead further.
Rattled Cardiff Blues needed a response and got it in some style as Samoa international Rey Lee-Lo arched a run to break clear before drawing the last men and sending centre partner Allen over to score in the corner for a clinical effort. Patchell added the touchline conversion.
Visiting fly half Thomas slotted a penalty just before the mid-point of the half as the game continued to rattle along at pace.
A series of penalties stopped the flow only briefly and Scarlets went further ahead just before the half hour mark as James Down was penalised for not rolling away and Thomas did the rest.
Scarlets threatened again when Gareth Owen ripped ball and burst up field before more slick handling put Thomas and then van der Merwe into space as missed tackles hurt the home side.
Fish juggled and then collected a kick ahead from Michael Collins, but the penalty count was beginning to cause the hosts issues and stop and momentum being built.
One last lineout drive before half-time, as Scarlets were caught offside, saw Lewis Rawlins yellow carded for illegally dragging down the rolling maul. But the visitors held out for a 20-10 lead at the break.
A tense and nervy start to the second half from the home side saw Scarlets almost move further ahead as they dominated territory in the opening minutes, despite being a man down, and looked to pounce on any further mistakes.
But it was Cardiff Blues who finally struck first in the second half as Number Eight Manoa Vosawai charged up field and bounced off tackles to win a penalty.
With a free ball and penalty secured, the backs slung it wide and a rapid and marauding James powered down the line before flicking a perfectly timed pass inside to Fish to dot down.
The home side were visibly growing in confidence as they kicked to the corner and tried to drive once more.
Navidi powered up the middle before Cardiff Blues looked to go wide and were stopped by the hand of Steff Evans who was yellow carded for a deliberate knock-on.
The home side immediately went to the corner, again had it dragged down and this time back row Emyr Phillips was yellow carded as Scarlets were suddenly reduced to 13 men in three chaotic minutes.
The roof then almost came off the stadium as hooker Dacey bulldozed over from the next lineout drive to tie the game. And Patchell then knocked over the difficult conversion for the lead with 23 minutes left.
Incredibly a man down the visitors hit back as they dominated territory for several minutes, kept the phases going and finally broke over with livewire scrum half Davies touching down and darting under tackles close to the line.
A grandstand finish from the home side saw the forwards pick and go around the fringes, as Cardiff Blues kicked to the corner and looked to drive once more.
James was next to race down the line and cause panic before Allen, Navidi and Reed all went close before pressure told as Cuthbert hit the line and powered over under the posts to secure the win.
03m Patchell p 3-0
07m Owens t Thomas c 3-7
12m Van der Merwe t Thomas c 3-14
16m Allen t Patchell c 10-14
18m Thomas p 10-17
28m Thomas p 10-20
49m Fish t 15-20
57m Dacey t Patchell c 22-20
67m Davies t Thomas c 22-27
77m Cuthbert t Patchell c 29-27
Cardiff Blues: 15 Dan Fish (Evans 70), 14 Alex Cuthbert, 13 Cory Allen, 12 Rey Lee-Lo, 11 Tom James, 10 Rhys Patchell, 9 Lloyd Williams; 1 Gethin Jenkins (Hobbs 23-29, 65), 2 Kristian Dacey (E Lewis 68), 3 Taufa’ao Filise (D Lewis 54), 4 Jarrad Hoeata (Reed 71), 5 James Down, 6 Josh Turnbull, 7 Josh Navidi, 8 Manoa Vosawai (Cook 65)
Replacements: 16 Ethan Lewis, 17 Sam Hobbs, 18 Dillon Lewis, 19 Lou Reed, 20 Macauley Cook, 21 Tavis Knoyle, 22 Jarrod Evans, 23 Garyn Smith