Recent Ireland debutant Tom Court and Nigel Brady have been named on the bench as the front row replacements.
Phoenix Ulster Rugby Academy player Ian Whitten moves up from the bench, where he started against Dragons, to replace shoulder injury victim Paul Steinmetz at inside centre.
Isaac Boss starts at scrum half with Cillian Willis providing back-up on the bench. Chris Henry retains his starting place at the base of the scrum while Robbie Diack is recovering from injury.
Bryn Cunningham has also been ruled out due to injury.
Speaking about Saturday's game, Williams said: "The individuals in the team have to take responsibility.
"We need a performance against Glasgow, and nothing but 100 percent will do.
"Our focus is to take back the points we lost against Dragons, and show what we are really capable of.
"The players all know that they have to stand up and perform come Saturday."
ULSTER (v Glasgow Warriors): Clinton Schifcofske; Andrew Trimble, Darren Cave, Ian Whitten, Simon Danielli; Ian Humphreys, Isaac Boss; Justin Fitzpatrick, Rory Best (capt), BJ Botha, Ryan Caldwell, Ed O'Donoghue, Matt McCullough, David Pollock, Chris Henry.
Replacements: Nigel Brady, Tom Court, Carlo Del Fava, Kieron Dawson, Cillian Willis, Niall O'Connor, Mark McCrea.