Fly half Rhys Priestland contributed 17 points, including a try, while wing Darren Daniel, No.8 David Lyons and full-back Dan Evans also crossed.
The Scarlets led 20-3 at the break and were always in control although a raft of changes disrupted the flow to allow the Warriors back in the game briefly. Worcester scored two late tries but Mike Ruddock's side never seriously threatened to win the game.
Replacement Ryan Lamb kicked a penalty five minutes from time to give London Irish their first win of their Anglo-Welsh campaign as they ground out a 12-11 victory against Cardiff.
Irish led 6-3 at the break thanks to a penalty apiece from Tom Homer and Peter Hewat, with Ceri Sweeney kicking a penalty for Cardiff Blues.
Hewat and Sweeney exchanged penalties after the interval before a Richie Rees try put the Blues 11-9 ahead, but Lamb stepped up to seal the win with Sweeney missing a tough long-range penalty in stoppage time.
South African Luke Watson announced his arrival with a debut try that swung the game, as Bath overcame Ospreys 21-11 in their clash at the Rec.
Watson drove over from a scrum for the opening try before Justin Tipuric replied for the Ospreys, but Daniel Browne made sure of the Bath win, with Ryan Davies converting to add to his three penalties.
Newport Gwent Dragons pushed Leicester Tigers all the way but came away empty handed from Welford Road. In an error-strewn game, Paul Turner's side lost 29-20 to a Tigers side which included eight internationals.
Jason Tovey to step inside the cover - reminiscent of Ieuan Evans' famous try for Wales in 1988 against Scotland - and go under the posts.
Jason Tovey and Aled Brew tries gave the Dragons an unlikely 12-11 lead at the break but Anthony Allen dotted down within two minutes of the re-start. A penalty try followed for the home side. Rhodri Gomer-Davies hit back for the Dragons to bring the visitors just three points behind but two Toby Flood penalties put the Tigers clear.
The LV= Cup Results
Cardiff Blues 11-12 London Irish
Newcastle 8-19 Harlequins
Wasps 21-14 Gloucester
Bath 21-11 Ospreys
Leicester 29-20 Newport-Gwent Dragons
Northampton 19-3 Saracens
Scarlets 32-17 Worcester