The reigning European champions went into their clash with their RaboDirect PRO12 rivals knowing that a win would keep them in pole position for a home quarter-final when the knockout stages get underway.
And despite some worrying moments for the Irish outfit second-half tries from Ireland internationals Rob Kearney and Isaac Boss proved the difference.
Duncan Weir kicked 11 points for the Warriors who briefly threatened an upset in the first half and Schmidt could not hide his delight at leaving Scotland with four points in the bag.
"I'm delighted to get that result," he said. "We knew the game would be a battle of attrition and that's pretty much the way it proved.
"I know there were imperfections in the performance and I know my players have gone on record saying I'm always fussy.
"I don't really care about the imperfections after that game. I just think we deserve to be proud of what we did.
"We deserved to get the four points and we'll come away from this, glue ourselves back together in six days' time and front up at the RDS in front of a full stadium and try to chase that home quarter-final that we really, really want."
In a first half dominated by Glasgow Leinster werel fortunate to go in level at 6-6 at the break, Weir notching twice for the home side whil Jonathan Sexton and Fergus McFadden were on target for Leinster.
But after the break the Irish outfit began to assert themselves and hit the front when Kearney collected a chip over the top from Sexton to race clear and score.
McFadden's penalty then extended the visitors' lead before replacement scrum-half Colin Gregor dived over to bring Glasgow right back into the game.
But despite the home side applying most of the pressure in the late stages it was Leinster who killed the game off when Boss wriggled over for the winning score.
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