Kearny ran in the opening try of the match in the 42nd minute to put Leinster into the lead. McFadden kept his composure to score the resultant conversion.
McFadden went on to add another penalty eight minutes later, only for Colin Gregor to reduce the arrears moments later with a try that was converted by Weir.
Reigning European champions Leinster ensured their qualification to the knockout stages when Boss scored a try in the 68th minute. Again, McFadden was on hand to score the conversion to seal the victory.
The loss has seen Glasgow knocked out of the competition.