Consistent kicking in tricky conditions from fly-half Matthew Morgan backed up Walker's effort to ensure the hosts secured their fifth consecutive league victory, moving them up to fifth.
In the first meeting between the two sides since last season's RaboDirect PRO12 final Leinster got the scoring underway after just three minutes when fly-half Ian Madigan slotted home a penalty.
And the European champions nearly scored the first try four minutes later as a great box kick from Isaac Boss found space behind the Ospreys' defence but Fionn Carr failed to gather the ball before sliding out of touch.
However from the resulting line-out Rhys Webb's kick was charged down and the rebound fell kindly to Leo Auva'a who touched down to give Leinster a 10-0 lead inside the opening ten minutes after Madigan added the extras.
That was to be the end of their scoring as Ospreys fought back with three first-half penalties, the first of which came after a quarter of an hour as Morgan relieved the early pressure.
The conditions were not helping either side as Morgan lost his footing when trying to find touch from his own half but from the next phase of play he made amends, converting another penalty.
On 34 minutes Leinster looked to capitalise on their best field position since the early exchanges after a clever Boss line break, chased well by Andrew Conway, led to a scrum five metres out.
But after Lloyd Peers had conceded the penalty, coming in at the side, Madigan missed the relatively straightforward kick albeit having to deal with the adverse conditions.
And, with the last action of the first-half, Morgan scored his third successive penalty, responding well to the visitor's early domination to bring Ospreys within one point.
At the start of the second period Ospreys had a chance to take the lead for the first time but after Morgan missed Leinster were straight onto the attack earning a penalty of their own which saw Duncan Jones sin-binned.
Although Madigan missed from the halfway line he broke through the Ospreys defence shortly after but a crucial tackle from Webb stopped him metres from the try line.
On the hour the 14 men took the lead for the first time as Morgan took a quick throw to Fussell who then ran straight through the middle before releasing Walker.
Morgan made his conversion to make the score 16-10 as Jones came back onto the field and from that point on Leinster began to chase the game.
But failing to find the momentum and penetration that had served them well at the start of the game they were unable to take away any points from advanced positions.
And Ospreys extended their lead through a Morgan drop goal with just six minutes remaining as they held out comfortably to ensure they remain unbeaten against the Irish side at the Liberty stadium since 2009.
|Ospreys Score Card|
|Leinster Rugby Score Card|