The Tigers desperately wanted revenge for their 15-3 away defeat but at the end of a pulsating first half they held a narrow 14-11 lead.
After weathering an early Scarlets storm, which produced a penalty for fly-half Rhys Priestland, Leicester scored 14 points without reply before the visitors staged a marvellous fightback.
Leicester scored two tries, through Miles Benjamin and Jordan Crane to one by Scarlets Rob Evans. Both Leicester’s tries came from line-outs in the Scarlets 22, the first a real statement of intent as they turned down the chance of an easy penalty to go for the try.
England flanker Tom Croft won the line out and after giant prop Logovi’i Mulipola had made a dent in the Scarlets defence a swift passing move resulted in Benjamin crashing through. Burns’ touchline conversion made it 7-3 in the 10th minute and five minutes later it was 14-3 after Croft again won a line out and Crane was driven over by the forwards, Burns again converting from the touchline.
Priestland pulled three points back with a 20th minute penalty but Mulipola should have had try number three for the Tigers five minutes later but knocked on near the line.
Priestland was causing Leicester all sorts of problems but it was a yellow card for lock Graham Kitchener, a fifth minute replacement for the injured Brad Thorne, which let Scarlets back into the game.
Scarlets took advantage, driving to the line following a line-out before Evans broke off to force his way over. Priestland missed the conversion.
Leicester scored try number three six minutes after the break and again it came after they turned down the chance of an easy penalty.
This time they went for a scrum in front of the posts and after good work by Crane and scrum half Ben Youngs, Thompstone scored in the corner. This time Burns missed the conversion.
The all-important fourth try came six minutes later, again from a line-out and drive, with replacement hooker Youngs scoring moments after coming on. Burns added the conversion to make it 26-11.
Youngs got a second after a lovely break by brother Ben, Burns again adding the conversion.
Scarlets hit back with a try by winger Harry Robinson but Steven Shingler missed the conversion. Scarlets were reduced to 14 men in the 65th minute when Aaron Shingler was sin-binned but while he was off the park Robinson scored his second try, converted by Steven Shingler.
Leicester scorers: Tries: Benjamin, Crane, Thompstone, T. Youngs 2, Harrison. Cons: Burns 4, O. Williams.
LEICESTER: Tait, Thompstone, Goneva, Baikeinuku, Benjamin, Burns, B. Youngs, Rizzo, Ghiraldini, Mulipola, Thorn, Parling, Croft, Salvi, Crane.
Replacements: Smith for Benjamin (73), O. Williams for Burns (62), Harrison for B. Youngs (62), Ayerza for Rizzo (51), T. Youngs for Ghiraldini (51), Balmain for Mulipola (54), Barbieri for Salvi (62).
Scarlets scorers: Tries: R. Evans, Robinson 2. Cons: S. Shingler. Pens: Priestland 2.
SCARLETS: J. Williams, Robinson, King, S. Williams, Parkes, Priestland, A. Davies, R. Evans, Elias, Adriaanse, Ball, Earle, A. Shingler, Barclay, McCusker, J. Davies.
Replacements: W. Jones for R. Evans (65), Rawlins for Earle (63), J. Davies for Barclay (57), Pitman for McCusker (63), Harris for J. Davies).
Referee: Pascal Gauzere (France).
European Rugby Challenge Cup Pool 1: Cardiff Blues 104 Rovigo 12
European Rugby Challenge Cup Pool 4: Bordeaux-Begles 26 London Welsh 3.