Edinburgh made it three home wins in a row to step up their quest to finish in the league's top eight and clinch a knock-out cup place.
Dougie Hall and Mike Blair scored first-half breakaway tries to put the Scots in control.
Chris Paterson added two conversions and a penalty to give Edinburgh a commanding half-time lead.
Scarlets had their chances but failed to capitalise and Paterson added two second-half penalties.
Scarlets had the better of the lively opening exchanges and winger Tal Selley looked certain to break the deadlock with a 40-metre dash, only to be thwarted by a Hugo Southwell tap tackle.
Llanelli kept up the pressure, but found themselves adrift following an interception by Simon Webster deep inside his own 22 zone.
Webster was blocked out five metres from the target, but the ball was spun out to Dougie Hall via Paterson and the hooker was left with an easy path to the line.
Paterson slotted the conversion and then added a well-struck penalty after the Welshmen were accused of illegally hauling down a line-out.
Edinburgh took advantage of another interception to claim try number two, Blair's powers of anticipation leaving him with a cruise to the line from 30 metres out to give Paterson a formality of a kick for the extra points.
After the break Edinburgh and Paterson added two further penalties to complete the scoring.
Edinburgh: H Southwell, C Paterson, M Di Rollo, B Laney, S Webster, P Godman, M Blair, A Jacobsen, D Hall, C Smith, F Pringle, S Murray, T Blackadder (capt), A Strokosch, D Callam.
Replacements: A Kelly, A Dickinson, N Hines, S Cross, R Lawson, C Joiner, D Lee.
Scarlets: G Evans; A Havili, M Watkins, M Phillips, T elley; G Bowen, D Peel; P John, R McBryde, J Davies, V Cooper, D Duley, S Easterby (capt), I Boobyer, A Powell.
Replacements: Dorian Williams (Llandovery), A Gravelle, C Wyatt, A Jones, J Mills, Arwel Thomas, S Finau.