The Heineken Cup champions, who are targeting a unique league and cup double, appeared on course for a comfortable victory in Newport thanks to a Jack McGrath try and the boot of Ian Madigan.
Darren Edward’s men fought back with tries at the death from Dan Lydiate and Will Harries but they left themselves too much to do with the final whistle ending their hopes of finishing the season on a high.
It was an emotion-packed evening at Rodney Parade as the Gwent outfit bid farewell to a host of loyal servants including France-bound duo Luke Charteris and Aled Brew, and Lloyd Burns, who was forced to retire last month.
Madigan fired Leinster into an early lead at Rodney Parade with a pair of penalties either side of an effort from Lewis Robling for the hosts.
The fly-half continued to punish the undisciplined Welsh region but the Dragons fought back with a thundering break from Toby Faletau.
Leinster did well to concede just the penalty and they extended their lead after a neat Noel Reid pop-pass allowed McGrath to crash over.
Madigan added the extras but failed with a long-range penalty at the death as Leinster entered the interval with a 16-6 lead.
Schmidt’s men weathered a Dragons storm following the break and should have grabbed a second try following a silky Madigan break.
But Carr was unable stamp his mark on the game, knocking on Madigan’s miss-pass with a clear run to the try line.
The fly-half was on target with a pair of quick-fire penalties as full-time approached to extend Leinster’s lead to 22-6.
But the Dragons refused to throw in the towel and were given a glimmer of hope when Lydiate rumbled over from close-range.
They continued to feed off a vocal crowd and Will Harries squeezed over at the death but it was too little too late.
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