In truth though, it was the conditions which won out, with neither team able to put in place sustained periods of attack.
Both sides welcomed back talismanic players, with Sean O'Brien starting at No.8 for Joe Schmidt's side and DTH van der Merwe on the wing for the Warriors.
However with the sodden conditions it was not the ideal environment for either O'Brien's trademark charges or van der Merwe pacy breaks.
Instead it was a real arm wrestle up front but despite edging the second half, Glasgow struggled to make the most of their possession.
Leinster had the better of the opening exchanges, and duly took the lead through fly-half Madigan with a fifth-minute penalty.
While the Irish side looked the more dangerous, Glasgow were defending resolutely, however after seeing off a succession of Leinster attacks on their own line, they were dealt a blow when Tom Ryder was sent to the sin bin.
The lock couldn't resist when Isaac Boss had the ball at the back of a ruck and knocked it out of the Irish international's hands.
However Madigan missed the ensuing penalty to leave the score at 3-0 to the visitors.
With torrential rain and a bitter wind tryscoring opportunities were at a premium and it was made even harder for Glasgow when Chris Fusaro was sin-binned for going off his feet ten minutes into the second half.
Madigan slotted the subsequent penalty to double the Leinster lead only for Glasgow to earn a penalty of their own three minutes later.
Peter Horne made a complete hash of that effort, the ball bouncing harmlessly under the posts, and he was off-target again four minutes later.
Replacement Scott Wight took over the kicking duties but to no greater success, missing his first effort just after the hour.
Glasgow appeared to be in the ascendancy but with handling difficult and a heavy pitch they were not able to turn their possession into points.
In the final minute Leinster were reduced to 14 men when Madigan was sent to the sin bin for a professional foul.
Despite the extra man, Glasgow failed as they had all game to take advantage, and they knocked the ball on with time up to slip to only their second home defeat to Leinster in five years.
|Glasgow Warriors Score Card|
|Leinster Rugby Score Card|