Ireland flanker Stephen Ferris returns following a hand injury, while Italy lock Carlo Del Fava, centre Ian Whitten and scrum-half Paul Marshall have also been brought into the starting XV.
"Glasgow are a powerful side, who will be out for a home win so we must be 100% on our game from start to finish," said Williams.
"I was bitterly disappointed with our last performance - we lost another game we should have won.
"We cannot talk our way out of it, or make excuses for how we played. Once again we were leading heading into the last 10 minutes, and lost a game we shouldn't have.
"Every player knows they have to put in a performance against Glasgow, both individually and as a team. Our focus is to take back the points we lost against Ospreys, and show what we are really capable of."