Having missed out on a place in the Ireland squad for the RBS 6 Nations match against Scotland, Madigan looked eager to prove a point as a half-time replacement at the RDS.
He was involved in Leinster's most potent attacks as they scored 21 unanswered points after the break, with Madigan converting tries from Aaron Dundon, Jordi Murphy and John Cooney.
Andrew Goodman did all the scoring in the opening 40 minutes for Leinster, his try and two penalties guiding them to a 11-5 lead.
Andy Fenby swooped for a Scarlets try in the 35th minute but they were overrun by the in-form hosts with turnovers proving costly for the Welsh region.
The first quarter was pockmarked by penalties but both sides showed an eagerness to attack from deep and put the ball through hands.
Leinster edged ahead in the third minute with New Zealander Goodman, assuming the kicking duties for the night, planting a penalty through the posts.
The Scarlets' young half-backs Owen Williams and Aled Davies probed for openings off the fringes of rucks, however Leinster were alive to the danger.
The visitors were reduced to 14 men after lock George Earle was carded for dangerous play at a lineout. Goodman though was unable to convert the resulting penalty.
Williams also sent a penalty chance wide just past the midway point of the first half.
Simon Easterby's men boxed clever while Earle was off the pitch, keeping their defensive line intact apart from a Fionn Carr and Dominic Ryan-inspired surge.
Leinster began to build some momentum after a direct run from number eight Murphy. A clever backhanded pass from Isaac Boss released David Kearney and their combined efforts led to Goodman's second three-pointer of the night.
The Kiwi then opened his try account for the province, swatting away Williams' attempted tackle to score in the right corner.
The pace and distribution skills of Carr, Kearney and Andrew Conway were to the fore in the build-up, with Goodman unable to convert from the touchline.
The Scarlets hit back straight from the restart, retrieving possession and hunting out to the left where Aaron Shingler and Aled Thomas combined to send Fenby streaking over in the corner.
Williams' conversion attempt went wide and Leinster also missed a couple of kicks closing in on half-time, Noel Reid hitting the left upright from closer range and Goodman pushing an effort wide.
Leinster used their lineout maul to good effect on the restart. A Shane Jennings drive to the line was ruled inconclusive, however hooker and man-of-the-match Dundon piled over from a similar attack soon after.
Madigan converted to put 11 points between the sides and just as the game seemed to be petering out, the out-half inspired Leinster's late bonus point push.
With 10 minutes left, Murphy took a great line onto a crisp pass from Cooney to score to the left of the posts with Madigan adding the extras.
Right at the death, Leinster turned defence into attack as Madigan and Fergus McFadden drove them on and replacement scrum-half Cooney sniped over from a close-range ruck to confirm the bonus point.
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- Andrew Goodman