The Irish province, who have pulled clear of Cardiff Blues at the league's summit, created a series of chances with young winger Luke Fitzgerald and scrum half Chris Keane enjoying some mismatches in midfield.
The Ospreys took their time to gel together and that was understandable given that only winger Nikki Walker and prop Paul James survived from the team that started the New Year's Eve victory over Cardiff.
Out to impress watching Ireland coach Eddie O'Sullivan, Jamie Heaslip caught Mike Phillips with a great wrap-around tackle and together with Cameron Jowitt, he drove the Wales scrum half back ten metres.
Keane make a great break around the side of a ruck in the sixth-minute, catching Hale T-Pole flat-footed, and while Heaslip was up in support, the attack petered out with Jonathan Sexton's pass to Felipe Contepomi a poor one.
Leinster were getting closer and closer to the Ospreys' whitewash - another chance went begging in the ninth-minute when the flying Fitzgerald just failed to hold a pass from Girvan Dempsey, wide out on the left flank.
Sexton then missed a chance to open the scoring with his right-sided penalty drifting to the left of the posts and the visitors began to make an impression, but their tactic of testing Gary Brown under the high ball never really paid off.
Stephen Keogh was stopped just short of the Ospreys' line. However, just when it looked like Leinster might fail to break the try deadlock, flanker Shane Jennings popped up with the opener in the 25th-minute.
Phillips was whistled up for preventing a quick ruck release, the penalty was kicked to touch and a quick line-out catch and drive, initiated by Malcolm O'Kelly, saw the Leinster pack barrel forward for Jennings to touch down.
Contepomi converted into a deceiving wind and Leinster's second try soon followed. Their captain Brian O'Driscoll, who looks to be rediscovering his form, secured possession in midfield and good hands out to the left put Fitzgerald dashing past T-Pole and Andrew Lloyd.
The blue shirts piled forward with Contepomi taking the ball on and Fitzgerald cut across in support to pass for the ever-ready Heaslip to dive over under the posts.
Contepomi's conversion was cancelled out by a Shaun Connor penalty, eight minutes before the interval.
With Leinster's concentration levels dipping, the Ospreys sensed their chance. Phillips took a quick tap and a couple of phases later, Connor spotted a hole on the blindside and taking a flat pass, the fly half cut past the stranded Heaslip and Brian Blaney to cross in the left corner.
With their lead cut to six points, Leinster put the Ospreys back under immediate pressure. Dummy runners caught the Welsh side out and a swift pass from Contepomi to Keogh put the former Munster man over for a try.
Contepomi's hooked conversion missed the uprights, leaving Leinster with a 19-8 buffer for half-time. Contepomi missed two penalty chances on the restart but with the Ospreys still struggling to make headway, the men in blue were still on top.
The visitors then lost Phillips to a needless yellow card, he was sent to the sideline for stamping on a Leinster player's leg just before he cleared from an Ospreys' ruck, and Leinster were soon over for the bonus point try.
A midfield switch between Contepomi and O'Driscoll created extra space for the latter to link with Dempsey and the fullback's pass sent Fitzgerald over in the left corner.
Contepomi added the conversion before he was replaced and despite some clever kicking from the on-form O'Driscoll, who combined well with Fitzgerald, and some midfield surges, Leinster could not unlock the Ospreys defence again.
Things seemed to click for the visitors in the closing stages. A solid 60th-minute break from Gareth Owen got the Welshmen on the front foot and Phillips, one of the players being closely watched by new Wales Coach Warren Gatland in the stands, was stopped just short of the whitewash.
Aided by the inclusion of the strong-running Filo Tiatia for the closing stages, the Ospreys enjoyed a better share of territory and after a concerted spell of pressure, flanker Ben Lewis piled over the line in the 77th-minute from just metres out.
Connor converted for a 26-15 scoreline and the Ospreys came searching for a try which would net them a losing bonus point for the trip home.
They won a penalty on the Leinster 22, ran it with time running out and a better placed pass to Aled Brew out on the left might have seen the Cardiff-born speedster get over.
Leinster lost replacement prop Stephen Knoop to the sin-bin for killing the ball but the home side reasserted themselves in injury time, ending the match in the Ospreys' 22 and holding firm for their fourth win in their last five encounters with Lyn Jones's side.