The men from Llanelli crossed three times after the break to come out on top through Steff Evans, Steff Hughes and Ryan Conbeer. Tom Rogers had already gone over in the first half.
After a convincing win over Nottingham last Saturday, this was a confidence-boosting result for Scarlets head coach Peel against a Tigers side which featured several England internationals.
It will leave Peel in good spirits ahead of his team’s first United Rugby Championship game which comes against Edinburgh at the end of the month.
Fielding a side containing 11 internationals of their own, the Scarlets shot out of the blocks and were over for the game’s first try inside five minutes.
Sam Costelow put in a clever chip which was gathered by centre Tyler Morgan. Scrum-half Kieran Hardy then took a sharp tap to take his side within sight of the whitewash.
As the pressure piled on, it was Rogers, who had come off his right wing, who picked up and found a space in the Tigers defensive wall to dive over.
Costelow was wide with the conversion and the Tigers’ response was swift.
A 50:22 kick from England fly-half George Ford saw Tigers claim the line-out throw in the visitors’ red zone and a strong surge from new captain Ellis Genge paved the way for centre Matt Scott to cross.
Ford landed the simple conversion.
Scarlets continued to have the better of possession and territory, but spilled possession at crucial moments as they pressed for the line.
Costelow landed a 40-metre penalty to regain the lead for the visitors, but a Ford strike ensured the Tigers held a narrow 10-8 advantage at the break.
It didn’t take long for Leicester to extend their lead at the start of the second half with hooker Tom Youngs crashing over after Scarlets lock Tom Price had been shown a yellow card for a breakdown penalty.
Ford converted, but the home crowd weren’t comfortable for long as Scarlets stunned the Tigers faithful with an impressive double-strike.
The outstanding Johnny McNicholl sliced through to set up an attack finished in style by Evans.
Then Hardy burst from the base of a ruck before feeding replacement Hughes for a free run to the line.
Dan Jones converted both to make it 22-17 but after the Scarlets failed to gather the restart, Tigers struck again through substitute prop Nephi Leatigaga.
Ford’s touchline conversion set up an intriguing final quarter as both sides emptied their bench.
The Scarlets weren’t done, however.
Some slick handling out wide freed replacement Conbeer and the flying wing did the rest for his fourth try in two games.
Jones again nailed the conversion to seal the win.