Hall replaces Fergus Thomson who is available for selection among the replacements. The same is true for Muldowney who is given the nod ahead of Tom Ryder. Rob Dewey comes in for Federico Aramburu who is unavailable for selection due to a neck strain.
Looking ahead to the game, head coach Sean Lineen said: "It was a challenging game [the Magners League play-off] down there in May, but we've got a fairly new squad now.
"The Ospreys have quality right throughout and they'll have an international XV whoever they pick."
Focussing on their particular areas of strength, Lineen singles out the Ospreys' defence as well as their ability to select from a plethora of talent and experience.
"The Ospreys defence is the strongest in the league and that is where they score their tries from - turnovers. Their set-piece play is very aggressive and they boast so many wily campaigners who can turn a game."
Lineen's selection caps off a particularly pleasing week for Hall who was among eight Warriors called up to the Scotland squad for the forthcoming Autumn Tests.
The 31-times capped hooker said: "I was aware I had to earn back my place in the Glasgow team and I'm glad some of my performances have given me the opportunity to start. I'm now looking forward to building on them.
"For me, this weekend is another opportunity to find a bit of form going into the Autumn Tests and hopefully gain selection.
"Nothing has been nailed down yet for the first game [against the All Blacks on 13 November] so hopefully Andy Robinson and the rest of the coaches will be at Firhill on Sunday. It means that if you were to put your hand up then you have a great chance of being involved."
With some focus now shifting towards the autumn internationals, Lineen knows that his players are now competing not only for places in a competitive Glasgow squad, but an opportunity to represent their country against some of the best sides in the world.
"I would like to think that they'll try even harder," he continued, "because there are places now up for grabs ahead of the All Blacks game."
Glasgow Warriors team to play the Ospreys in the Magners League at Firhill on Sunday 24 October (kick-off 4.10pm)
15 Bernardo Stortoni
14 DTH van der Merwe
13 Max Evans
12 Graeme Morrison
11 Rob Dewey
10 Ruaridh Jackson
9 Colin Gregor
1 Jon Welsh
2 Dougie Hall
3 Moray Low
4 Richie Gray
5 Aly Muldowney
6 Robert Harley
7 John Barclay CAPTAIN
8 Richie Vernon
Substitutes: 16 Fergus Thomson, 17 Kevin Tkachuk, 18 Ed Kalman, 19 Tom Ryder, 20 Calum Forrester, 21 Henry Pyrgos, 22 Duncan Weir, 23 Peter Horne
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