The 31-year-old has not played for club or country since sustaining a neck injury while playing for Scotland in the Autumn Nations Cup, with his last outing for the Warriors having been in the 20-7 win over the Scarlets at Scotstoun back in October.
Adam Hastings also returns from his three-match suspension for the must-win tie, lining up at full-back for Danny Wilson's side.
Brown's inclusion is the only alteration to the front-row that started last weekend's win over the Ospreys, as Aki Seiuli and Enrique Pieretto continue as the starting props.
An all-new second-row partnership sees Kiran McDonald promoted from the bench to the starting XV, joining the returning Richie Gray in the engine room.
The back-row is unchanged, as Robert Harley and Tom Gordon line up either side of number eight Ryan Wilson.
Sean Kennedy retains his place in the starting lineup at scrum-half, whilst Ross Thompson continues at fly-half after his impressive Player of the Match-winning performance against the Ospreys.
The midfield pairing of Robbie Fergusson and Nick Grigg is once again given the nod by Wilson, with the duo having provided a solid defensive presence in last weekend's victory.
Lee Jones and Rufus McLean - both try-scorers last time out - are retained as the starting wingers, as Hastings returns from his red card-enforced layoff to start in the 15 jersey.
There is a welcome return amongst the replacements for the club's most experienced back, as Peter Horne returns following a lengthy spell on the sidelines with concussion.
Grant Stewart rotates to the bench after starting each of the club's last four outings, joining Dylan Evans and D'arcy Rae as the front-row replacements.
Similarly, Leone Nakarawa moves to the replacements to accommodate the returning Gray, whilst Fotu Lokotui is set for his first involvement in a Glasgow matchday 23 since scoring against the Dragons at Scotstoun back in December.
A brace of the club's young talents complete the squad, as Jamie Dobie and Ollie Smith wear numbers 21 and 23 respectively.
Speaking following selection, Head Coach Danny Wilson told glasgowwarriors.org: "After two wins on the bounce, we go away to an inform and almost full strength Dragons, with only a couple players away to Wales.
"Our destiny is in our own hands this weekend and a win on Sunday will give us a chance to qualify for the European Champions Cup next season.
"We reward form and once again this weekend's team includes a number of our young players who have been going well as well as a number of experienced players coming back to us."
14 Rufus McLean
13 Nick Grigg
12 Robbie Fergusson
11 Lee Jones
10 Ross Thompson
9 Sean Kennedy
1 Aki Seiuli
2 Fraser Brown
3 Enrique Pieretto
4 Richie Gray
5 Kiran McDonald
6 Robert Harley
7 Tom Gordon
8 Ryan Wilson (Captain)
Substitutes
16 Grant Stewart
17 Dylan Evans
18 D'arcy Rae
19 Leone Nakarawa
20 Fotu Lokotui
21 Jamie Dobie
22 Peter Horne
23 Ollie Smith
Unavailable for selection: Alex Allan, Scott Cummings, Cole Forbes, Chris Fusaro, George Horne, Patrick Kelly, Johnny Matthews, Tommy Seymour, Kyle Steyn.
International duty: Matt Fagerson, Zander Fagerson, Sam Johnson, Huw Jones, Oli Kebble, Ali Price, George Turner.