Alex Dunbar returns to partner Sam Johnson in midfield, outside a brand-new half back combination of Henry Pyrgos and Peter Horne.
The back-three remains unchanged, DTH van der Merwe and Tommy Seymour starting either side of Stuart Hogg.
Alex Allan and Zander Fagerson start either side of Fraser Brown in the front row.
Scott Cummings comes into the boiler room, joining Jonny Gray.
Callum Gibbins captains the side named on the open-side flank with Rob Harley occupying the number 6 jersey and Matt Fagerson is at Number 8.
Meanwhile, Oli Kebble sustained an ankle injury in the game against Scarlets which will rule him out for the remainder of the season.
Ryan Wilson sustained a chest injury in the same game and is expected to be unavailable for the next few weeks.
Glasgow Warriors Head Coach Dave Rennie said: "It was a pretty flat performance last week. We created opportunities but our lack of accuracy saw us convert just one of our seven line breaks. Against quality sides, you'll get punished.
"Connacht lead the competition in ball carries with the ability to look after possession for long periods of time. It will be a great test of our defensive resilience.
"Alex and Fraser come back in. We have some real quality in midfield at our disposal, and Alex gets a crack this week. He has trained and prepared really well for the past few weeks so I'm looking forward to seeing him back in a Warriors jersey.
"Fraser has been dogged with injury, the most recent an ankle injury against Italy. His experience and physicality will be welcomed."
15 Stuart Hogg
14 Tommy Seymour
13 Alex Dunbar
12 Sam Johnson
11 DTH van der Merwe
10 Peter Horne
9 Henry Pyrgos
1 Alex Allan
2 Fraser Brown
3 Zander Fagerson
4 Scott Cummings
5 Jonny Gray
6 Robert Harley
7 Callum Gibbins (Captain)
8 Matt Fagerson
Substitutes
16 Grant Stewart
17 Jamie Bhatti
18 Siua Halanukonuka
19 Kiran McDonald
20 Chris Fusaro
21 Ali Price
22 Finn Russell
23 Nikola Matawalu
Not available due to injury: Adam Ashe (ankle), Oli Kebble (ankle), Patrick Kelly (ankle), Pat MacArthur (shoulder), Leonardo Sarto (shoulder), Tim Swinson (thigh) and Ryan Wilson (chest)