Jack Dempsey is the only member of the back-row to retain his place from last weekend's victory at Scotstoun, as Tom Gordon replaces the injured Rory Darge at openside and Gregor Brown comes in at blindside after a knock to Matt Fagerson in midweek.
Tom Jordan makes his third successive start at fly-half as he partners skipper Price in the half-backs, the former Ayrshire Bull sitting in the league's top 10 for offloads after the first two rounds.
On the bench, double centurion Ryan Wilson is in line for his first outing of the season, having been named as part of a six-two split of forwards and backs by the club's coaching team.
Simon Berghan and Sean Kennedy are similarly in line for their first action of the campaign, with Kennedy set for his first Glasgow Warriors appearance since April's victory over Zebre Parma at Scotstoun.
Speaking following selection, Franco Smith told glasgowwarriors.org: "Last weekend's performance against Cardiff was another step forward in our journey - our systems clicked and we won playing our brand of rugby.
"Tomorrow we want to make another step forward when we take on an experienced Ospreys side.
"It's great to be able to bring Sam, Rufus and Gregor into the starting XV. They alll have worked hard in training and have earned their chance to pull on the jersey tomorrow afternoon.
"Ospreys have threats across the park and once again we will need to be ruthless in the contact area and clinical in attack in Swansea tomorrow."
15 Cole Forbes
Unavailable for selection: Rory Darge (ankle), Allan Dell (calf), Jamie Dobie (hamstring), Matt Fagerson (rib), Huw Jones (back), Nathan McBeth (knee) Ally Miller (back), Enrique Pieretto (shoulder), Kyle Steyn (hamstring), Max Williamson (shoulder)