Head Coach Danny Wilson makes seven changes in total from last weekend's victory over Zebre Parma, as the Warriors look to make it four successive wins in the 2021/22 United Rugby Championhip.
Fagerson's inclusion is the only alteration to the front-row, as the British and Irish Lion comes into the starting lineup to pack down alongside Jamie Bhatti and Johnny Matthews.
Robert Harley will make his first start of the season after being selected in the second-row alongside Richie Gray.
Jack Dempsey comes back into the squad after missing the trip to Italy last weekend, with the number eight part of a triumvirate completed by captain Ryan Wilson and openside Rory Darge.
Behind the scrum, Duncan Weir partners the returning Lion, Price, in the half-backs, having contributed seven points with the boot last weekend.
Sam Johnson comes back into the midfield at inside centre, which sees Sione Tuipulotu shift to outside centre after scoring his first try for the club in Parma last time out.
Rufus McLean - who leads the league in clean breaks and sits second for metres gained - is the only member of the back three to retain his place, with Kyle Steyn and Ross Thompson completing the starting XV.
The replacements see a trio of internationals provide the front-row cover, as Scotland duo George Turner and Oli Kebble are joined by Argentinian tight-head Enrique Pieretto.
Lewis Bean wears the number 19 jersey, whilst Matt Fagerson covers the back-row after missing last weekend's win due to illness.
George Horne and Nick Grigg each rotate to the bench after starting in Parma, as does Cole Forbes, who starts amongst the replacements for the first time in his Glasgow career.
Speaking following selection, Head Coach Wilson told glasgowwarriors.org: "We're pleased to be able to welcome our British and Irish Lions back for tomorrow's match.
"Both Ali [Price] and Zander [Fagerson] have trained well since returning to our environment and both men are eager to play their part for the team.
"Leinster will be a big test for our squad - they've been the benchmark for the rest of the competition in recent years and we know they'll present a physical challenge tomorrow night.
"It's important for us to finish this first block of fixtures in the right manner, and we want to build on our three straight wins ahead of the international window."
14 Kyle Steyn
13 Sione Tuipulotu
12 Sam Johnson
11 Rufus McLean
10 Duncan Weir
9 Ali Price
1 Jamie Bhatti
2 Johnny Matthews
3 Zander Fagerson
4 Robert Harley
5 Richie Gray
6 Ryan Wilson (Captain)
7 Rory Darge
8 Jack Dempsey
Substitutes
16 George Turner
17 Oli Kebble
18 Enrique Pieretto
19 Lewis Bean
20 Matt Fagerson
21 George Horne
22 Nick Grigg
23 Cole Forbes
Unavailable for selection: Simon Berghan, Fraser Brown, Scott Cummings, Tom Lambert, Kiran McDonald, Ewan McQuillin, Ratu Tagive