Williams crossed for the second of those scores with less than two minutes remaining to set up Dan Biggar's successful conversion that handed the visitors a 31-30 success in Dublin.
"I enjoy success of course like anybody else. The one you remember is the latest one and this is a great way for me to finish," admitted Williams as the Ospreys were crowned PRO12 Champions for the second time in three years.
"It's nice to be retiring with some silverware. This is up there with anything else I have achieved.
"I am very proud of the fact that I am associated with the Ospreys. We have worked very hard this season, we have had our ups and downs and there has been a lot of change in the ranks, with a lot of players leaving the region.
"For us to stick at it the way we have is a compliment to the guys. I will never forget this day."
Williams has a knack of signing off in style having done the same with both Wales and the Lions.
The 35-year-old's final appearance for Britain and Ireland's elite came in the record-equaling victory over the Springboks in the third Test three years ago.
Having been left out of the starting line up for the first two internationals in South Africa, Williams scored twice in a 28-9 win over the then World Champions as the Lions picked up their first Test victory in eight attempts.
His stellar career with Wales ended in similar fashion as well as he dotted down for his 58th try for his country with the final play of December's defeat to Australia.
The former IRB World Player of the Year will now be hoping for more of the same this Saturday when he plays for the Barbarians against Wales in Cardiff in what will be his final match as a professional.