An opportunist brace from Isa Nacewa appeared to put the European Champions on course to complete a sensational double.
But Welsh record try-scorer Williams had other ideas and grabbed two late tries to inspire the Swansea-based outfit to their fourth league crown.
The Ospreys made an encouraging start at the RDS and Dan biggar edged the Welsh region into a 6-3 lead.
But Leinster quickly got into the form that secured them the Heineken Cup and some sublime footwork from Brian O’Driscoll sent Sean Cronin over.
Biggar hit-back with the boot but the Ospreys switched off at the restart and Nacewa collected Sexton’s kick to race clear. Sexton converted to put Leinster 17-9 up.
Leinster had prop Heinke Van Der Merwe binned and were twice warned by referee Romain Poite for collapsing a series of eight scrums scrums before getting a crucial decision in injury time.
That had the Ospreys management jumping in frustration on the sidelines and sparked a brawl between players as both teams left the field at half-time.
But the Ospreys came out fighting after the break and a barnstorming charge from Joe Bearman set-up Beck to score.
Biggar added the extras to bring the Ospreys within a point but Sexton kept the scoreboard ticking over for the hosts and they led 23-16 with an hour remaining.
But cometh the hour cometh the man and Williams demonstrated his deadly finishing to hand the Ospreys a glimmer of hope with his first.
Nacewa grabbed his second in the final ten minutes and the PRO12 silverware appeared out of reach. But the Ospreys pack flexed it’s muscle again at scrum-time and this time Nathan White was sent to the sin-bin.
And with full-time approaching and the Ospreys hammering at Leinster’s blue wall Williams skipped past two defenders to sign off from regional rugby in sensational style.
Biggar demonstrated nerves of steel to slot the difficult conversion and despite a gut-wrenching final few minutes the Ospreys held on for glory.
