Exeter Chiefs were made to work hard by a determined Scarlets team at Sandy Park.
The Chiefs looked in total control after early converted tries from Ian Whitten and Simon Alcott.
But James Hanks' yellow card allowed Scarlets back into the match - with the visitors just seven points behind at the turnaround.
Scott Williams' try at the start of the second half levelled the scores, but the Chiefs won the game thanks to a Gareth Steenson penalty and a last minute James Scaysbrook converted try.
Elsewhere today, the Cornish Pirates won at Swansea by 30 points to 10 in the British and Irish Cup.
Kyle Marriott, Tom Bedford and Rob Elloway scored tries for the visitors.