They had needed to beat the Cardiff Blues and for the Ospreys to lose in Aironi, but the defending champions' 12-10 victory in Viadana was enough to put them through.
The Scarlets gave a start to centre Regan King in his final match for the region before he joins French club Clermont Auvergne, while injuries meant the Blues were forced to play Jamie Roberts on the right wing.
Honours had been shared at the end of a dramatic first half with the sides locked together at 20-20. During a dramatic opening 40 minutes of changing fortunes, both sides scored two tries.
In the first quarter the Scarlets took a 13-3 lead with by a try from prop Iestyn Thomas who finished off a drive from a lineout.
That was after Blues lock Michael Paterson had been sent to the sin-bin following a late challenge on fly-half Stephen Jones.
But the Blues came back with a converted try from winger Chris Czekaj, who was sent over by Roberts, and a Dan Parks penalty.
And 13-13 soon became 20-20 as both sides scored tries within two minutes of each other. Ben Morgan scrambled over after slipping a tackle and Dafydd Hewitt took advantage of some sloppy Scarlets defence when he escaped from a double tackle.
Parks failed with a drop goal attempt at the end of the first half but he made amends with a successful effort in the second minute as the Blues got their noses in front for the first time.
But David Young's side suffered a setback when number 8 Xavier Rush was taken from the pitch on a stretcher following a clash of heads with Scarlets prop Rhys Thomas.
And after Parks missed a penalty shot, the Scarlets regained the lead when winger Sean Lamont went in down the left for an unconverted try. It was a double blow for the Blues as Martyn Williams was also sin-binned for a professional foul.
After Priestland landed a penalty to take the Blues out of losing bonus point territory, the Scarlets scored their bonus point try through Lamont.
But any victory celebrations for the hosts were tempered by news that the Ospreys had finished fourth in the table, setting up a semi-final showdown with Munster in Limerick.
|Scarlets Score Card|
|Cardiff Blues Score Card|