Warriors edged a thrilling 38-34 clash with Cardiff last weekend but their Kiwi coach is concerned about the number of points his men shipped against Blues.
And he warned they may find themselves breaking down if they make a repeat against this weekend’s Irish visitors to Scotstoun.
Rennie said: “Connacht are going to bring over a pretty well-oiled team with a lot of experience.
“They’ve been going really well and because of how tight the comp is this is a big game for both sides.
“They play a pretty good brand of footy and we know they’re going to ask a lot of questions of us, so we’re going to have to be a lot better this week than we were against Cardiff.”
George Horne returns from injury to start the Guinness PRO14 clash. Horne has been sidelined since Glasgow’s Heineken Champions Cup clash against Saracens in January and partners Brandon Thomson at half-back.
Paddy Kelly is brought into the midfield for his first Warriors start as he doubles up with fellow centre Stafford McDowall.
Niko Matawalu missed Glasgow’s victory in Cardiff with a head knock but has successfully passed his return to play protocols to start on the wing this Friday night. Ruairdh Jackson and Kyle Steyn join him in the back-three.
Oli Kebble has recovered from a sickness bug to start in the front-row and Siua Halanukonuka starts the other side of hooker Grant Stewart.
Tim Swinson and Scott Cummings continue their partnership in the second-row and behind them Chris Fusaro returns from injury to captain the side. Rob Harley and Adam Ashe are the other loose forwards selected to start.