Williams will be feeling confident following from three Ulster victories in recent weeks over Munster, Portugal and Cardiff Blues 'A'.
There are only three points separating Ulster and Connacht in the Magners League table and with Ulster focused on climbing the league over the next few months, this game is crucial for the province's aims.
They welcome back Ireland internationals Stephen Ferris, Rory Best and Paddy Wallace for this crunch game, as well as Scotland winger Simon Danielli, who has returned to fitness following a knee injury picked up during the pre-season.
Williams said: "We have a lot of respect for Connacht, they are a good side and play a hard game of rugby but we are more determined than ever and we are going out to win.
"We have performed well in our last few games - we won our last two Magners League games and beat a spirited Munster side.
"We will not hide from this Connacht side. The guys are hungry to play and continue on from the Munster and Portugal games and we hope that the Ulster Rugby public know how much this game means to us and get out and support us."
Connacht's last victory over Ulster was a 22-12 success in Galway in the league on New Year's Eve 2005, however they have not won in Belfast since a 6-3 victory on November 16, 1960 in the Interprovincial championship.
ULSTER Squad (v Connacht): Backs (13) - Niall O'Connor, Bryn Cunningham, Timoci Nagusa, Darren Cave, Andrew Trimble, Ian Whitten, Cillian Willis, Isaac Boss, Paul Steinmetz, Ian Humphreys, Mark McCrea, Paddy Wallace, Simon Danielli.
Forwards (13) - Justin Fitzpatrick, Rory Best (capt), Nigel Brady, Tom Court, BJ Botha, Ed O'Donoghue, Ryan Caldwell, Matt McCullough, Kieron Dawson, Robbie Diack, Stephen Ferris, David Pollock, Thomas Anderson.