And having been denied in similar circumstances a year ago against Munster, Leinster were desperate to back up their European win over Ulster last weekend.
After a good start from the Ospreys, the Irish side settled into their groove with tries from Sean Cronin and Nacewa giving them an eight-point lead at the break at the RDS.
However the Ospreys were showing the form that saw them cruise past reigning champions Munster in the semi-final and fought back thanks to a try from Ashley Beck.
Two penalties from Jonathan Sexton appeared to be taking the game away from the Ospreys only for Williams to score his first of the game in the corner.
But again Leinster stepped it up when they had to as Nacewa grabbed his second but when Nathan White was sent to the sin bin, Williams popped up to score his second try and Biggar held his nerve to win the game.
The Ospreys made the quicker start and Biggar made no mistake with his first effort from wide on the left to give the Ospreys the first points of the game, but Sexton responded immediately to level things up.
Biggar added another penalty to make it 6-3 but Leinster had looked the stronger side up to then and eventually the pressure told as they took advantage of poor control at the back of a strong Ospreys scrum to set up Cronin.
Leinster mounted a series of attacks before Brian O'Driscoll showed some great footwork and handed the ball on to Cronin who went through a gap in the Ospreys' defensive line to score the opening try. Sexton's conversion made it 10-6.
With seven minutes remaining in the first half the Ospreys scrum, which proved the stronger all game, got the better of their Leinster counterparts and Biggar carried on his perfect kicking display to make it 10-9.
But the Ospreys then switched off completely from the restart and Nacewa claimed Sexton's kick to sprint over unchallenged for Leinster's second try. Sexton found the target to put Leinster 17-9 up with four minutes left in the half.
The Ospreys responded with a couple of powerful scrums on the Leinster line and loosehead Heinke van der Merwe was sent to the sin bin. But despite two more scrum penalties the Irish side held out to lead 17-9 at half-time.
The visitors were clearly frustrated but came out flying in the second half and Beck collected a great offload from Joe Bearman to sprint in from the 22 despite the attentions of Sexton. Biggar added the simple conversion to bring the Ospreys back to within a point.
However again the Ospreys failed to deal with the restart and conceded a penalty straightaway which Sexton slotted to stretch the lead back to four.
With Leinster restored to a full complement they earned another penalty which Sexton knocked over from 30 metres out as the Irish side led 23-16 with half an hour remaining.
Just before the hour the Ospreys used the ball off the back of a lineout and sent it wide where Williams showed his finishing ability to race over in the corner despite the attentions of Eoin Reddan. But Biggar missed the conversion to tie it.
That stung Leinster into action and after a loose pass from Jonathan Sexton deep inside the Ospreys 22, Nacewa reacted quickest to grab his second try.
But when the Ospreys scrum again got on top, White was sent to the bin, and with the Ospreys on the attack Williams slipped between two tackles to dot down in the right corner.
Biggar's conversion attempt could not have been more difficult but the fly-half showed nerves of steel to split the uprights.
And despite some late drama as the Ospreys failed to kick the ball out with the 80 minutes up, the Welsh side got the ball back to win the title for the second time in three years.
