They fell further behind when slick hands from Richardt Strauss and Luke Fitzgerald gave Nacewa enough space to skip by Chris Czekaj for a try he converted himself.
Parks knocked over two successive penalties to close the gap, with Casey Laulala beginning to cause problems for the Leinster defence. But the hosts tightened their grip on proceedings, moving 20-6 clear for the break courtesy of a penalty brace from Nacewa.
The same player put in a try-saving tackle on Richard Mustoe as Cardiff began the second half with intent. Scrum half Rees had sparked a superb counter attack out of the 22, and the Blues' new-found adventure was soon rewarded. Parks punted a penalty to touch, and lock Davies muscled his way over off the next phase.
Parks added the extras and after Leinster failed to convert a couple of promising attacking situations, the Blues squared the game at 20-20 thanks to a terrific team try.
Laulala's long pass set up an overlap on the right and a couple of well-timed deliveries from Davies and Mustoe sent Xavier Rush charging into the 22. The Cardiff skipper's brilliant offload out of the tackle then put Rees in behind the posts and Parks comfortably converted.
The Scotland international tagged on a penalty for good measure and suddenly Leinster were behind. But Schmidt's men were up for the challenge and they bounced back to deservedly take the spoils.
Replacement prop Cian Healy drew two defenders on a barge through the middle to tee up McFadden for a sprint in under the posts.
Nacewa converted and in the final minute, took his personal tally to 19 points as he topped off Madigan's fine snipe from outside the 22 which took the losing bonus point away from the Blues.
Reflecting on his first victory as Leinster coach, Schmidt commented: "We created a few chances in the second half, but every time they attacked they seemed to have numbers out wide.
"If we take our opportunities it will take the pressure off us. I'm really pleased to get the win and I felt that the guys coming off the bench gave us that little bit extra.
"It was difficult for Ian Madigan to come on and play so late into the build-up but I thought he did well and credit to him for stepping into the breach. If you had offered me a bonus point before the game, I would have scrambled over hot coals (for it)!
"The bonus point was a bit fortuitous at the end but I'm delighted to be on the blue side of a win, for the first time. I thought that we showed nous and a lot of character out there and it was overall a really good effort."
Giving his reaction, Cardiff boss David Young said: "Going into half-time, we knew, if we could keep the ball, get a bit of field position and a platform we could cause them problems. We certainly did that and it was a massive disappointment we did not win after taking the lead.
"There was a penalty which could have gone either way but went to Leinster. And we have got to look at our defence because their last try was all too easy.
"Even if they had a penalty, we would have come away with a bonus point. We had a tough time at the scrum with two young props in Tom Davies and Scott Andrews, but they have got to learn.
"They will get better with this experience. We wouldn't be talking about them if we had come away with a win."
|Leinster Rugby Score Card|
|Cardiff Blues Score Card|