Exeter outside half Gareth Steenson was the chief architect of the Scarlets downfall, kicking 17 points to steer his side to a 16-22 victory in Pool Five.
The Chiefs got off to a flying start when scrum-half Haydn Thomas scored a try on five minutes – it was a lead they would never relinquish.
Steenson was on target again to extend the Chiefs lead to 10 points after the Scarlets were caught offside from an Aled Davies box kick.
The Scarlets eventually got themselves in a good attacking position but knocked the ball on at a ruck with Andy Fenby isolated. But from the resulting scrum the Scarlets earned a penalty which Rhys Priestland converted.
Chiefs responded with a third Steenson penalty after the Scarlets found themselves under pressure at the scrum to go in at the break 16-6 ahead.
The Scarlets suffered a major setback when Priestland was carried off after picking up an ankle injury when he slipped when in possession. He was replaced by Aled Thomas.
Things went from bad to worse for the Scarlets as Steenson was on target with his fourth penalty on 49 minutes.
Thomas kicked a fine long range penalty but that was cancelled out four minutes later with Steenson’s fifth penalty as the Chiefs led 22-9 on the hour mark.
But despite their lead the Chiefs were forced to defend their 22 and in the process lost prop Ben Moon to the sin bin for collapsing a scrum.
And with the extra man the Scarlets earned a penalty try to cut the Chiefs lead to 22-16 but despite hammering at Exeter’s 22 the visitors held on for a famous win.
