The Irish side needed just a point from their game on Friday night to ensure they reached the knock-out stages for the tenth time in 13 years.
And with the scores at 3-3, their job was made easier when Ospreys lock Ian Evans was red-carded for an alleged stamp on 20 minutes, after which Leinster took control.
Two penalty tries plus scores for Cian Healy, Jordi Murphy and Isaac Boss did the damage, with Jimmy Gopperth kicking four conversions and a penalty to secure top spot in Pool 1.
Current RaboDirect PRO 12 leaders Munster were already guaranteed a quarter-final berth but ensured it would be a home clash with Toulouse after beating Edinburgh 38-6.
The Irish side ran in six tries - through James Coughlan, Johne Murphy, Conor Murray, Peter O'Mahony, Simon Zebo and Felix Jones - as Edinburgh's European run came to an end for the season.
Ulster also secured a home quarter-final after ending Leicester Tigers' 25-match unbeaten run at home in the competition with a narrow 22-19 win.
South African Ruan Pienaar was the star man, scoring all of his side's points including charging down Toby Flood's kick for a decisive try.
While in the European Challenge Cup, any hopes of having a RaboDirect PRO12 representative in the knock-out stages came to an end.
Cardiff Blues came up just short in their bid to qualify as best runners-up from the European Cup, losing to Pool 2 opponents Exeter Chiefs 19-13.
Alex Cuthbert dotted down, while Leigh Halfpenny kicked eight points to ensure a losing bonus point, but with results elsewhere not going their way over the weekend, their European hopes were dashed.
Glasgow Warriors also brought the curtain down on their European adventure finishing bottom of Pool Two, despite a gutsy display against Toulon.
Chris Fusaro scored the only try of the game but five penalties from the boot of Jonny Wilkinson saw them lose out 15-8.
Elsewhere Ben Botica's late penalty for Harlequins ended any Welsh involvement in Europe as Scarlets succumbed to a 22-20 loss while Connacht conceded 11 tries away to Saracens to lose 64-6.
Italian sides Zebre and Benetton Treviso had already been knocked out of the European Cup but failed to end their campaign on a high, losing 16-6 and 24-6 to Toulouse and Montpellier respectively.
Meanwhile Newport Gwent Dragons brought their European Challenge Cup run to an end with a 24-12 win over Rugby Mogliano to finish second in Pool Two behind Bath Rugby.
TRY OF THE WEEKEND
They may have conceded the game's first points through Greig Laidlaw's penalty but Munster were always too good for Edinburgh and bounced back immediately with a cleverly-worked team try.
Straight from the restart, Paul O'Connell rose highest to gather Ian Keatley's kick before a series of quick interchanges across the pitch saw James Couglan dart through into space and touch down.
From then on it was all Munster as they secured their home quarter-final with ease.
BREAK OF THE WEEKEND
The stakes were high for the Scarlets heading into their clash with Harlequins with a battle for the final place in the European Challenge Cup quarter-finals.
And they got off to the perfect start thanks to a thrilling counter-attack try inspired by Rhys Priestland inside his own half.
The fly-half set winger Jordan Williams free to make a superb break before passing to Gareth Davis to race in and score.
Two further tries followed and Scarlets were heading through before Ben Botica's penalty three minutes from time dashed all hope.
PLAY OF THE WEEKEND
Three-times European Cup winners Leinster showed off the incredible power of their pack against Ospreys, twice being rewarded with penalty tries after punishing driving mauls.
And they were equally adept as individuals as, following a line out on the far side, Jack McGrath eventually gathered before pushing his way forward.
With the ball being recycled it was Ian Madigan's turn to drive towards the line and although being stopped just short, Jordi Murphy ably picked up the baton to barge over late on.
PLAYER OF THE WEEKEND
With both teams competing for the crucial home quarter-final game, it was always going to be a close one between Leicester Tigers and Ulster and so it proved with Ruan Pienaar cancelling out Toby Flood's hat-trick of penalties for a 9-9 half-time score.
But the South African got the upper hand on his opposite number in the second half, charging down Flood's kick to score his side's only try before converting to draw the scores level.
After the game captain Johann Muller hailed his teammate's efforts and the confidence he gives the team.
And with his fifth penalty giving his side a dramatic win, there is no doubt as to his worth to the team.
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