Horne is preferred to Finn Russell who is on the Glasgow bench after a disappointing performance in last weekend's defeat to Scarlets.
Head coach Dave Rennie told The Scotsman: "It was Finn's first game back in. We are going into the business end of the season and I want them to understand that regardless of reputation we are just going to play guys that we think will do the job for us.
"To be honest to win it (the PRO14) we need Finn playing at his best. He was a couple of shades off it last week. Horney is a pretty accomplished ten as well and he gets a crack this week. Hopefully Finn comes off the bench and plays well.
"Finn is pretty clear on expectations. He is desperate to leave this club with another title. Ultimately you are judged by your performance and judged by your preparation. If guys don't perform as expected you have two options. You give them another crack or you apply pressure by showing confidence in others.
"We have lots of competition for places and Finn has had a pretty good run with Scotland starting every game so we are keen to give Horney a start."
Alex Dunbar has recovered from a hamstring injury and starts alongside Sam Johnstone in the midfield.
"We have really good depth in midfield," said Rennie. "I think Sam Johnson has probably been our best midfielder throughout the year and you have to find a place for him going into the business part of the season and that leaves four other international midfielders to fill two of those spots and with Peter Horne able to play ten and twelve that leaves just one other.
"Alex Dunbar has recovered from injury, he's been available the last couple of weeks. He's trained really well and we looked closely at putting him in last week but Nick Grigg's form has been excellent. So, yeah, Nick's unlucky that he is out of the mix this week but Alex is good to go and it's tough for Hugh (Jones).
"He's had a really good attacking campaign for Scotland, he's certainly a high quality finisher. He is working really hard on his defensive game and training hard and he might get an opportunity next week but it's hard to fit them all in, dammit!"