With two games left to play the west Walians are still in with a mathematical chance of winning the title, although they would need three of the teams above them to lose all their remaining matches.
Stephen Jones launched the Stradey try-fest with a diagonal run to the posts inside the Edinburgh 22 and then the visitors gifted the home side two long range tries when Watkins intercepted from 70 metres out and Regan King snapped up a dropped pass from similar range to race clear.
The Scottish side, coached by former Cardiff Coach Lyn Howells, got back into the game just before the break with a try from prop Allan Jacobsen, which cut the gap to 11 points at the interval, but there was to be no denying the Scarlets.
Scott MacLeod pounced for a try against his fellow countrymen and then Watkins danced his way to a second try. Iestyn Thomas completed the rout courtesy of a try scoring pass from fellow prop John Davies.
The Scarlets host the title-chasing Cardiff Blues at Stradey Park on Saturday in another crucial game.
Scarlets: Tries: M Watkins (2), S Jones, R King, S MacLeod, I Thomas. Cons: S Jones (5), C Thomas
Edinburgh: Tries: A Jacobsen, D Callam. Con: P Godman. Pen: P Godman
Scarlets: M Stoddart; D Daniel, R King, M Watkins, M Jones (G Evans 21); S Jones (C Thomas 60), L Davies (C Stuart-Smith 74); D Manu (I Thomas 57), K Owens (M Rees 57), J Davies, V Cooper, S MacLeod (I Afeaki 71), D Jones, J Bater, A Popham (N Thomas 71)
Edinburgh: B Cairns; R Dewey, M Di Rollo (L Lopez Fleming 65), M Dey, S Webster; P Godman, G Laidlaw (J Senio 51); A Jacobsen, A Kelly (S Lawrie 67), G Cross (D Hewett 73), A Strokosch, F Pringle, S Taylor, A Hogg (R Rennie 63), D Callam
Referee: Peter Fitzgibbon (Ireland)