Dwayne Peel and Dafydd James went over early on as the Scarlets threatened to run away with the game having already bagged a place in the quarter-finals.
The Welsh region was forced to withstand a second-half fightback by the Exiles. However, Shane Geraghty's ten points, including his side's only try of the game, was not enough to stop the Scarlet tide sweeping into the last eight and gaining home advantage in the quarter-finals.
Playing against a stiff breeze, the Scarlets opened with a penalty from outside-half Jones that was cancelled out by opposite number Barry Everitt. The Scarlets pack created the opening score of the game, stealing a scrum off Irish to allow Peel to dart over early on.
James then galloped sixty-five metres from inside his own half for his twenty-seventh try in the competition after intercepting Geraghty's wild pass. Everitt pulled back a penalty to make it 17-6 at the break and the Exiles made a bright start to the second half, rewarded when Geraghty went over from close range.
Geraghty converted and added a sixty-sixth-minute penalty to close the gap to just a point before Jones eased the Stradey Park nerves with a huge penalty from the half-way line.
Topsy Ojo went close to snatching victory with a late break before Exiles lock Nick Kennedy was sin binned for punching Scarlets skipper Simon Easterby, who was left smiling when the final whistle finally sounded.