Robertson (calf) and Cross (ankle) both missed Boxing Day's bonus point win over the Warriors because of injury, but have recovered in time to play in the second leg.
After performing well in the first leg, lock Craig Hamilton has been rested for the trip west with Scotland internationalist Mustchin stepping in to fill the number four jersey.
Alan MacDonald, who recorded his 50th appearance for Edinburgh last Friday, comes in at openside flanker with Rennie side-lined and awaiting the results of his operation.
Head physiotherapist TJ Johansson said: "Ross underwent the operation today (Tuesday) to ascertain the full extent of the damage to his knee. We will wait for the results before determining how long his rehabilitation programme will last."
Despite achieving a 39-6 first leg victory over Glasgow, Edinburgh have not won at the Warriors for five years with four of the current starting line-up featuring in a 25-16 win - Allan Jacobsen, Allister Hogg, Hugo Southwell and Simon Webster.
As a result, wing Webster, who scored in Friday's bonus point win, said: "Games at Glasgow are always incredibly tough, but we are determined to achieve that elusive 'double' over them which has proved to be really difficult in the past."
Edinburgh Rugby Club squad to play Glasgow Warriors in the second leg of the David Lloyd 1872 Cup and Magners League at Firhill Arena (Friday 2 January, kick off 3pm)
15 Hugo Southwell
14 Mark Robertson
13 Ben Cairns
12 Nick De Luca
11 Simon Webster
10 Phil Godman
9 Mike Blair (captain)
1 Allan Jacobsen
2 Ross Ford
3 Geoff Cross
4 Matt Mustchin
5 Jim Hamilton
6 Scott Newlands
7 Alan MacDonald
8 Allister Hogg
Substitutes: Andrew Kelly, Gavin Kerr, Ben Gissing, Simon Cross, Greig Laidlaw, David Blair, John Houston.
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