In the first half Scarlets were the better team and would have pushed Worcester much harder had young outside-half Owen Williams not missed with three routine penalties at a crucial stage in the game.
Worcester took a third-minute lead when, from a ruck inside his own half, lock Chris Jones broke away on a 40-metre run. Scarlets were penalised and Carlisle put the hosts ahead with a 40-metre kick.
That was soon countered by a penalty for Scarlets kicked by Williams and after 11 minutes the same player added another to put the visitors ahead.
Back came the Warriors to tie the scores with a second Carlisle penalty but Scarlets regained the lead with an excellent try from Andy Fenby.
Warriors lost possession in their own 22 for Scarlets to counter-attack swiftly. A long pass from Owen Williams sent Kristian Phillips away and the wing ran 40 metres before kicking ahead to enable Fenby to pick up and score.
Williams converted to give his side a 13-6 lead by the end of the first quarter.
Scarlets continued to be the sharper side and should have extended their advantage but Williams was wide with a 25-metre penalty attempt.
Following a line-out in the Welsh 22, two players were sin-binned. Scarlets lock Joe Snyman received his yellow card for illegally pulling down Jones before Warriors captain Dean Schofield picked up his for retaliation in the ensuing melee.
Lethargic Worcester introduced Andy Goode at the interval in an attempt to rejuvenate the side, with Carlisle switching to centre in place of Jon Clarke.
Nikki Walker also departed in favour of Ben Howard.
Williams failed with a long-distance penalty attempt for Scarlets but Worcester had the better of the opening exchanges of the second half.
The hosts declined the opportunity to kick two simple penalties in favour of more attacking options and their pressure was rewarded with a try from replacement Howard which was converted by Carlisle to make it 13-13 with 25 minutes remaining.
Back came Scarlets but they missed a glaring chance to go back in front when Williams could not convert a penalty from 30 metres.
Again Worcester had a chance for points but neglected to kick for goal following a penalty award. Jonny Arr took a quick tap and the chance was gone.
The Warriors then produced their best handling movement of the game with Andy Short just being hauled in touch narrowly short of the line.
However the Warriors were not to be denied as replacement Semisi Taulava and Jake Abbott both drove over from line-outs close to the Scarlets line with the tries being converted by Carlisle to emphasise Worcester's second-half superiority.
Scarlets battled to the end and were rewarded when Phillips won the race for the touchdown following a 60-metre kick and chase but Warriors had the final say with a last-minute try from Neil Best converted by Carlisle.
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