However, second row Quinn Roux left the game with a worrying looking shoulder injury when he was sent sprawling to the floor from a lineout.
It could have been even worse. Leinster lost their opening two lineouts, the first to the anticipation of Glasgow's Tim Swinson, the second to Aaron Dundon's crooked throw.
But they followed this with a monster scrum that forced a penalty which out-half Ian Madigan smacked between the posts in the fifth minute.
There were many chances to improve their position, denied only by the simple mistakes that have muddied their season.
Glasgow tested the patience of Welsh referee Neil Hennessy on more than one occasion before lock Tom Ryder saw yellow for illegal work at a ruck.
As the drizzling rain fell, the mistakes kept coming all the way to the break, mostly from Leinster, because they had the vast majority of possession.
Consecutive uncharacteristic spills from wing Dave Kearney and full-back Isa Nacewa preceded a nice switch between O'Brien and Nacewa.
It forced Warriors captain Chris Fusaro into a blatant indiscretion that cost him their second yellow card, allowing Madigan to fire Leinster six ahead in the 50th minute.
Tight-head Jamie Hagan's high tackle and infringement at a scrum afforded centre Peter Horne two very kickable penalties. He couldn't take either one.
Replacement Scott Wright also missed a penalty when Jack McGrath infringed at a scrum, as Leinster moved up a place to fourth.