Steve Tandy’s men still had a faint chance of qualifying for the play-offs if results elsewhere went in their favour.
But the reigning champions failed to complete their part of the bargain as their season ended in disappointment.
Conway crossed twice in the opening quarter but the Ospreys fought back through Dan Biggar and Ben John.
But Conway completed his hat-trick shortly after the break and Cian Healy put the result beyond doubt despite Ashley Beck crossing for a try of his own.
The Ospreys’ season has been built around an unforgiving defence but Leinster quickly put them on the back foot with speed and slight of hand.
A fumble by Ospreys wing Ross Jones opened the door for Conway to collect Fergus McFadden’s chip. Sexton added the extras and Leinster exposed some uncharacteristic poor defending from Adam Jones to release Conway for his second.
Sexton’s conversion completed an emphatic opening period for home side, but Ospreys were in no mood to give up their title without a fight.
Biggar launched the comeback with a quick-tap to score and Tom Habberfield made the inroads for the Ospreys’ second. He surged into the Leinster twenty-two and the ball was spread to John to cross in the corner
Sexton had the final say in the half with a penalty seconds before the interval and within minutes of the restart the hosts had established a 12-point advantage as Conway completed his hat-trick.
Sexton kept the scoreboard ticking and Tom Isaacs crossed the whitewash to give the defending champions a glimmer of hope.
