Ulster will be looking to retain the focus and match-winning form that saw the side record a bonus point 37-11 victory over European champions Munster last Saturday at Thomond Park.
Only one point separates the Scots from Ulster in the Magners League table at present.
Williams has included all five of last Saturday's try scorers for selection for the Edinburgh trip, as well as man-of-the-match Ian Humphreys.
Scotland international Rob Dewey returns to the Ulster squad in time to potentially face his old club after featuring for the province's 'A' side earlier this week.
The Ulster squad has also been boosted by the return of lock Ryan Caldwell who has recovered from an ankle injury. Ulster and Ireland prop Bryan Young is also included as is versatile young back Ian Whitten.
Williams, who will name his starting line-up on Thursday, said: "What we did against Munster was a real achievement, but every match is a clean slate and we are going into this game with as much determination and focus as we did Saturday's and that means taking nothing for granted.
"There are no guarantees in this league and Edinburgh are a strong team with pace on the ball. They have shown their skills with a win over the current league leaders, the Ospreys.
"This is a critical game for both sides, and we all know it will be a tough contest to the final whistle."
ULSTER Squad (v Edinburgh): Backs (12) - Timoci Nagusa, Darren Cave, Andrew Trimble, Rob Dewey, Paul Marshall, Clinton Schifcofske, Ian Whitten, Isaac Boss, Paul Steinmetz, Ian Humphreys, Mark McCrea, Paddy Wallace.
Forwards (14) - Justin Fitzpatrick, Nigel Brady, Tom Court, BJ Botha, Bryan Young, Ed O'Donoghue, Matt McCullough, Kieron Dawson, Robbie Diack, Stephen Ferris, David Pollock, Rory Best, Ryan Caldwell, Filo Paulo.