The Ospreys were playing their third game in six days and had to be content with leaving the RDS with a losing bonus point after leading 16-10 at the break.
Having lost by a point to Biarritz Olympique in the Heineken Cup quarter-finals last weekend, the Ospreys had to travel to Ulster on Tuesday night. They took all five points in that game, but were outgunned in the second half against Leinster.
An interception try from wing Isa Nacewa gave Leinster a dream start, but 16 points from outside half Dan Biggar, including a try, saw the visitors' edge ahead by half-time.
Leinster coach Michael Cheika made five changes from their quarter-final line-up, while the Ospreys started with nine of the team that started in San Sebastian.
The Irish side increased the tempo of their game in the second half and could have taken the lead when Fergus McFadden lined-up two long range penalties, but the centre pushed them both wide.
But a clean break try from outside half Shaun Berne, which McFadden converted from in front of the posts edged Leinster back into the lead. McFadden then hit the mark with another penalty to give the home side some breathing space.
The Ospreys threw everything into the final stages, but then lost lock Ian Gough to the sin bin for a late charge on Berne.
Victory leaves Leinster needing just one more win from their final three matches to finish on top of the regular league table - and guarantee them a home tie in the Play-Off semi-finals that provide the gateway to the inaugural Magners League Grand Final the weekend after the Heineken Cup final in Paris.
Cheika's side have one more Magners League outing before they face Toulouse in the opening Heineken Cup semi-final in Toulouse on Saturday, 1 May. That will see them travel to Glasgow to meet the Warriors, another of the teams in the shake-up for a Play-Off place.