Simon Humberstone nudged Blues into a 9-6 lead at the break after a first half dominated by the boot of the two fly halves on show.
The visitors then took the lead at the start of the second half when flanker Sion Bennett touched down.
But skipper Jenkins led by example as his try on the hour proved decisive as Blues closed the cup game out to remain undefeated and in the mix for knockout rugby.
Blues were led out on the night by prop Taufa’ao Filise – as he made his 182nd
appearance to become the joint record appearance holder for the region.
However, it was Scarlets who settled the quicker with a successful early penalty from Josh Lewis.
Dan Fish produced a superb early kick to turn Jordan Williams as Blues looked to pick up where they left off in the north east of England and dominate territory.
Back row duo Ellis Jenkins and Rory Watts-Jones looked to carry forward with pace, but another penalty at the breakdown area saw early possession lost.
Humberstone was the next to kick deep into the corner, after a solid home scrum, and the fly half then had a chance to level the scores from out wide which he duly slotted.
A high tackle on Fish gave Blues more territory, after Jordan Williams had moments earlier run into a solid home defensive wall, but this time Humberstone saw his long range kick have the legs but not the accuracy.
A quick tap and go penalty from skipper Ellis Jenkins injected more pace into the game before Blues went over in the corner but were penalised for a double movement.
Both teams were working each over in the opening quarter looking for weaknesses but it was Scarlets who dominated possession for several minutes as they kept the ball alive and tested the Blues defence.
Eventually a kick in behind forced Blues to concede a penalty and Scarlets looked to drive over from the lineout but knocked on with the line closing in.
Lewis missed a long range penalty for Scarlets while his counterpart made no mistake with a sweetly struck effort for the lead.
Blues repeatedly looked to their driving game to assert some dominance, but a well-drilled Scarlets were frustrating them as they shut the door.
A break from Owen Jenkins, as he stepped off his right foot and away into space, secured another penalty that Humberstone slotted. But back came Scarlets with Lewis making it a three-point game at half-time.
Scarlets then struck at the very start of the second half as Lewis cleverly kicked in behind and the bounce favoured flanker Sion Bennett who touched down for a 13-9 lead.
They also had the chance to increase the lead further after a big scrum, but Lewis was narrowly off target with his penalty.
Blues needed something to fire them up and the home pack came to the party as they shunted Scarlets off their own ball at the scrum and then picked to the corner and not the posts to the delight of the crowd.
The initial drive was stopped but the ball was quickly fed right by the alert Tomos Williams to Jenkins and he smashed through tackles for the lead. Humberstone added the difficult touchline conversion.
Scarlets looked to hit back and only great scrambled defence from Blues stopped them doing just that, with Summerhill pouncing on the loose wide ball.
The young guns on the Blues replacements bench were fired into action as the half wore on, with Liam Belcher, Brad Thyer and Seb Davies all making debuts.
And it was fellow replacement Will Thomas who sparked yet more points as he made a line break and Scarlets flanker Bennett was duly yellow carded as he slowed up ball at breakdown.
The young fly half picked himself up and slotted the penalty for a 19-13 lead before blues showed great maturity in the dying minutes to see the game out and claim the win.
03m Lewis p 0-3
11m Humberstone p 3-3
30m Humberstone p 6-3
37m Humberstone p 9-3
39m Lewis p 9-6
43m Bennett t Lewis c 9-13
60m Jenkins t Humberstone c 16-13
74m Thomas p 19-13
Cardiff Blues: 15 Dan Fish, 14 Tom Williams (Davies 72), 13 Aled Summerhill, 12 Garyn Smith, 11 Owen Jenkins, 10 Simon Humberstone (Thomas 67), 9 Tavis Knoyle (Ts Williams 51); 1 Thomas Davies (Thyer 72), 2 Rhys Williams (Belcher 66), 3 Taufa’ao Filise (Andrews 51), 4 Miles Normandale (Davies 67), 5 Chris Dicomidis, 6 Jevon Groves (Roach 61), 7 Ellis Jenkins (c), 8 Rory Watts-Jones
Replacements: 16 Liam Belcher, 17 Brad Thyer, 18 Scott Andrews, 19 Seb Davies, 20 Ben Roach, 21 Tomos Williams, 22 Will Thomas, 23 Harry Davies