McFadden scored an eighth minute try, off a deft pass from fly-half Shaun Berne, and kicked 11 points with the boot as Leinster led 16-12 at half-time.
Blues winger Chris Czekaj crossed for an unconverted score in the opening minute of the second half, adding to earlier tries from prop Gary Powell and flanker Sam Warburton.
But Leinster regained the lead when hooker Bernard Jackman forced his way over the whitewash and the visitors sealed the deal with a Berne drop goal and a fourth and final penalty from McFadden.
Speaking after his side's nine-point win, Cheika said: "I was pleased that the younger guys who had an opportunity to play stood up quite well and even though there's so much to play for still, we're focused on the performance and we're pleased with how we went.
"We knew that we'd have to defend for long periods and then take our opportunities when they came and it was important for us to capitalise on the opportunities that came our way.
"Today we made a decision to play some of the younger players and the likes of Andrew Conway and Eoin O'Malley, who hasn't played a lot in the Magners League, did well.
"We haven't had a lot of continuity in the league so far this year, so we haven't been as fluent in our play - but we showed real character which is pleasing. It's a happy dressing-room in there, as it should be."
The Blues, who had won five in a row in all competitions, had an abundance of possession despite their troubles in the tight, but lacked the penetration to turn their free-flowing rugby into scores.
The game was marked by the first ladies day at Cardiff City Stadium, which saw Dai Young's side wearing pink to show their support for nominated charity, Cancer Research Wales.
But they got off to a disappointing start, going 10-0 down inside the opening 18 minutes. A turnover in midfield allowed Berne sent Isa Nacewa advancing up his wing and although Leinster were kept at bay, they recycled the ball and McFadden took an excellent angle to cross under the posts.
He added the conversion himself, followed by a penalty after the Blues had once again spilled the ball in their eagerness to play to an expansive style.
The home side finally got it right in the 20th minute when front rower Powell, later to leave on a stretcher with an Achilles injury, plunged over in the right corner, but another McFadden penalty kept Leinster in front at 13-5.
With the normally reliable Ben Blair off key in his place-kicking, the Blues opted to kick for position and it paid off when Warburton, released from Wales duty, dived over and Blair tagged on the extras.
McFadden landed another penalty with the last kick of the first half, but Cardiff began the second half in sparkling fashion. They moved the ball at pace, going right and then left where lock Scott Morgan beat an opponent and sent Czekaj over in the corner.
However, Cardiff's lead did not last long. A superb break by centre Eoin O'Malley took Leinster into the Blues' 22 and he found experienced hooker Jackman on his shoulder for a try which gave McFadden a simple conversion.
The Blues then lost fly-half Ceri Sweeney to the sin-bin for what was harshly ruled to be a spear tackle on opposite number Berne, but the home side managed to survive the 10 minutes without leaking any further points.
But Berne then dropped a goal which extended Leinster's advantage and robbed the Blues of a losing bonus point.
They seemed to have retrieved it when Sweeney kicked a late penalty after Leinster lock Devin Toner was yellow carded for a deliberate knock-on, only for key man McFadden to step up and slot over a penalty from halfway with the final kick of the game.
With his side now only two points ahead of the Scarlets in the race to secure Heineken Cup qualification, Blues boss Dai Young said: "We were under pressure coming into this game and we know it's going to go to the wire and I don't think that will change, but obviously we've got to pick up points with five games left.
"We've got to look to win all five, but we will have to be better than we were today because if we'd played anywhere like we had over the last six weeks it's a game we would have come away quite comfortably with."
He added: "We knew they were going to be very physical and try to force mistakes and pretty much play on the counter-attack or try and get penalties and that was pretty much what they brought to the table."
|Cardiff Blues Score Card|
|Leinster Rugby Score Card|