But it was Leinster's experience, led by Jonathan Sexton, which proved decisive, as Jamie Heaslip's first-half try edged them to a narrow win and a place in the final against Irish rivals Ulster in Dublin in a fortnight's time.
After the sides had felt their way into the game in the opening ten minutes it was Leinster, who will be back in Dublin on Friday night for the Amlin Cup final against Stade Francais, who took the lead as Sexton slotted a straightforward penalty.
But Joe Schmidt's side were dealt a blow almost immediately when Brian O'Driscoll was forced off with an injury, Andrew Conway replacing him and Fergus McFadden moving into the centres.
Glasgow were also forced into an early change as second row Tim Swinson went off with a blood injury, Tom Ryder coming on to replace him.
However the visitors looked far from overwhelmed, in their third semi-final in four years, and it was livewire scrum-half Nikola Matawalu who produced the game's first try on the quarter-hour.
After a series of attacks had brought the Warriors within striking distance, the Fijian picked and went off the back of a ruck and dotted down under the posts despite the attentions of the Leinster fringe defence.
Hogg slotted a simple conversion to put Glasgow 7-3 up, and it could have been even better for the visitors soon after as Rob Kearney brilliantly held up a rampaging Ryan Grant who looked certain to score.
Hogg did add another penalty soon after as Glasgow, with Swinson back on, appeared to have all the momentum on their side.
But Leinster have not reached the final in each of the last three years without knowing how to respond to pressure and they scored their first try just two minutes later.
A powerful rolling maul from an attacking lineout had the Glasgow defence at breaking point and as the Scottish pack faltered Heaslip peeled off the back to crash over despite the best efforts of Matawalu.
It got worse for Glasgow almost immediately as a storming run from Kevin McLaughlin had the Warriors scrambling backwards, and Matawalu was sent to the sin-bin when he was in the way of a pass while in an offside position.
Sexton slotted the resulting penalty to put Leinster back in front 11-10, and Glasgow were hit with another set-back when Josh Strauss had to be replaced, Ryan Harley coming on in his place.
The visitors managed to hang on until half-time though despite one moment of danger when Isa Nacewa looked set to collect Sexton's kick to score only to be beaten by the bounce of the ball.
Matawalu returned at the start of the second half and it was Glasgow who posed the first danger with a searing break from Peter Horne, but after he had chipped ahead Nacewa's incredible kick from the narrowest of angles cleared the danger.
But the game was becoming more open and it was Glasgow who appeared the more threatening, Sean Maitland stepping his way into the 22 only to lose the ball, and Hogg attacking the line at pace.
The Leinster scrum was on top, however, and that allowed them to take the steam out of the game, and just after the hour Sexton extended the lead with a penalty after Horne was penalised for crossing.
The Ireland fly-half had the chance to extend the lead further with another penalty attempt but his effort rebounded off the post.
Shortly after Leinster lost their second centre of the afternoon as Gordon D'Arcy had to be helped off the pitch, with Ian Madigan replacing him.
But another scrum penalty, just inside the Leinster half, allowed Sexton to put Leinster seven points clear at 17-10.
Glasgow looked to be fading but a stunning counter-attack saw Matawalu, now on the wing, sprint away down the left but despite some breathtaking offloads, Leinster held out until a knock on from John Barclay.
Deep in Leinster territory the Warriors reversed the trend in the scrum and earned a penalty, and after a barrage of attacks it was replacement centre Mark Bennett who crashed over with just five minutes remaining.
But with the chance to level the scores from wide on the right, Hogg's conversion drifted wide, to leave Leinster two points clear.
Still Glasgow continued to press but a knock on from Matawalu gave Leinster a scrum in the middle of the pitch and they earned a penalty to book a return to the ground on May 25 against Ulster.
|Leinster Rugby Score Card|
|Glasgow Warriors Score Card|