Stuart Hogg comes back into the side at full-back, as Tommy Seymour moves to the left wing, with Sean Lamont not involved this weekend. Australian international Taqele Naiyaravoro continues on the right wing.
Mark Bennett once again starts at outside centre, with Peter Horne coming in for Alex Dunbar inside him.
Finn Russell and Hart form this week's half-back partnership.
In the pack Ryan Grant returns at loosehead in place of Alex Allan, while Fraser Brown continues at hooker and Sila Puafisi is once again named at tighthead.
Leone Nakarawa and Jonny Gray continue in the Warriors engine room.
In the backrow Ryan Wilson comes in for the injured Rob Harley at blindside, Chris Fusaro replaces Simone Favaro at open-side and Adam Ashe starts at number 8, with Josh Strauss not included in the matchday squad.
Tickets for the Edinburgh leg of the 1872 Scottish Cup can be purchased online at glasgowwarriors.org during the festive period.
Glasgow Warriors head coach Gregor Townsend said: "The 1872 Scottish Cup matches are always highly anticipated encounters and we're really looking forward to Sunday's game.
"We must remain focused for the full eighty-minutes if we're to come away with a positive result and crucial GUINNESSS PRO12 points.
"It's great to hear that our supporters are travelling through to Edinburgh in large numbers to get behind the team, and their vocal support will once again give us a boost this weekend."
Glasgow Warriors team to play Edinburgh Rugby, GUINNESS PRO12 (1872 Scottish Cup, first leg), BT Murrayfield, Sunday 27 December (kick-off 3.05pm) - live on BBC ALBA:
15. Stuart Hogg
14. Taqele Naiyaravoro
13. Mark Bennett
12. Peter Horne
11. Tommy Seymour
10. Finn Russell
9. Grayson Hart
1. Ryan Grant
2. Fraser Brown
3. Sila Puafisi
4. Leone Nakarawa
5. Jonny Gray (Captain)
6. Ryan Wilson
7. Chris Fusaro
8. Adam Ashe
Replacements
16. James Malcolm
17. Gordon Reid
18. Zander Fagerson
19. Tim Swinson
20. Simone Favaro
21. Ali Price
22. Sam Johnson
23. Lee Jones
Not available due to injury: Mike Blair (concussion), Kevin Bryce (shoulder), Mike Cusack (ribs), Alex Dunbar (groin), Rob Harley (thumb), Tyrone Holmes (foot), Pat MacArthur (jaw), Henry Pyrgos (wrist), Fergus Scott (shoulder) and Richie Vernon (shoulder).
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