Ospreys scored a quickfire 21 points to decide a scintillating game - though it was not enough to ensure they will finish ahead of the Blues this year.
Danny Wilson's men are two points behind seventh-place Ospreys and will also leapfrog Edinburgh should they end their campaign on a high note at BT Murrayfield.
And Wales scrum-half Williams, who missed the Judgement Day clash due to injury, believes his side's new-found consistency is set to last.
"We want to end our season on a high against Edinburgh," he said. "We are waiting on results from other games but if we win our last game and do the best we can, hopefully we can climb the league and potentially finish above the Ospreys.
"We have to use this to push us on for next year. We have shown we can do better.
"It's been a season I have enjoyed. For various reasons we have been a bit inconsistent over the last four years but there's consistency now and there's no surprise that we're now getting better as a team."
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