The hosts were trailing 13-10 at the break but a blistering second-half display - led by wing Andrew Trimble - saw Williams and co finish three points clear of Leinster at the summit of the table.
Trimble scored twice, fly-half Ruan Pienaar finished with 22 points and Robbie Diack scored on his 100th appearance for the club on a perfect night for Mark Anscombe's troops.
But it will all be in vain unless Ulster claim the RaboDirect PRO12 trophy according to Williams.
"We play game to win silverware and for the great support we have here it would be great to bring some silverware home," said Williams.
"I don't even have to ask for the support, they will pull it out of the bag, they are unbelievable.
"Having the semi-final here at Ravenhill is a real joy, we're looking forward to it we'll enjoy the win. A few lads had milestones so we'll give them the praise they deserve, full credit to those.
"We just took ownership after half-time. We needed to get hold of the game, and the ball as well - I was guilty of losing the ball as much as anyone but we delivered in the second half.
"We'll have a quick look at the game, rest up the bodies and look at the blackboard on Monday."
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