A poor Leinster unit only came to life briefly in the second half but by then the Welshmen led by 24 clear points.
The effort was all the more impressive as the Ospreys were not just shorn of their international stars such as scrum-half Mike Phillips and prop Adam Jones, on World Cup duty, but there is already a long injury list for coach Scott Johnson to contend with.
Flanker Kevin McLaughlin made his 50th Leinster appearance, while the side was captained by number eight Rhys Ruddock, son of 2005 Wales Grand Slam-winning coach Mike Ruddock.
It did not take long for the Ospreys, who finished fourth last season, to get their campaign rolling with the first try of the season.
It was started and finished by scrum-half Rhys Webb after two minutes, who deservedly went on to get the man-of-the-match award.
He picked up from a ruck and, after the ball passed through the hands of centres Ashley Beck and Andrew Bishop, the number nine finished it off in the corner from 10 metres.
Outside-half Dan Biggar, who had booted the try conversion, increased the home lead with a penalty before video referee Neil Ballard ruled out a possible touchdown from big number eight Jonathan Thomas as the Welsh international back row had not put the ball over the line.
But there was no stopping the Welshmen as Leinster made little impression. They took a good 17-0 advantage when wing Hanno Dirksen, who was involved in the build-up to Thomas' effort, dived in at the left corner.
This time, Ballard looked at the replay and decided Dirksen did not put a foot in touch and awarded the touchdown that Biggar converted brilliantly.
It was one-way traffic as Biggar added a 15-metre drop-goal before Leinster stand-off Mat Berquist eventually got his side off the mark with a close-range penalty.
The Ospreys struck again before the interval when Webb broke from a ruck and chipped over the head of the defence for flanker and captain Justin Tipuric to grab and dive over.
Biggar converted and, at the break, it already looked like game over as the Ospreys led 27-3.
Leinster eventually woke up and got over the line after 50 minutes but McLaughlin's try effort was ruled out by video referee Ballard.
Tipuric did not help his side's cause by being shown a yellow card for a ruck offence but the Irishmen failed to take advantage and score while he was off the pitch.
Leinster were their own worst enemies too as they were turned over when in good attacking positions.
As neither side was able to score by any means in the second half, the only disappointment for the Ospreys was that they could not find a fourth try for a bonus point.
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