Leinster will go into the quarter finals of the URC off the back of a victory.
They edged a close encounter with Glasgow Warriors by 13 points to 5 at the Aviva Stadium.
A Jimmy O'Brien try and a penalty each from Sam Prendergast and Ciaran Frawley was enough to secure the win.
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Earlier, Connacht ended their season with a 22-12 win over Zebre.