The lightning-quick 25-year-old wing marked his first home RaboDirect PRO12 start since his summer switch from Connacht by continually carving up the Dragons defence - laying on the opening score for Eoin O'Malley before crossing for the final score of the night.
O'Malley was followed over the try line fly-half Ian Madigan as the Irish hosts stepped up a gear in the second-half to blow away their Welsh visitors.
Isa Nacewa also contributed 16 points with the boot to wipe away the memories of the opening 27-3 defeat to Ospreys and condemn the Dragons to a second successive loss.
With Jonny Sexton gearing up to face the USA for Ireland at the World Cup in New Zealand, Nacewa, who opted not to travel and represent Fiji, took over the kicking duties and slotted the first three points of the evening on six minutes.
Nacewa missed his second attempt two minutes later and Jason Tovey made no mistake when he was presented with the chance to level up the scores on 12 minutes.
After dominating the game up front on the early stages, Leinster began to cede ground to the Welsh visitors as the game reached the 25 minute stage deadlocked.
Leinster thought they'd gained the first try of the night when winger Carr's break allowed Nacewa to release Dave Kearney on the opposite flank only for the 22-year-old to be held up over the line.
Nacewa eased the disappointment by converting a penalty on 31 minutes and the scores stayed at 6-3 up until the break.
While Fijian Nacewa was leading the scoring with his boot Leinster's brightest spark was winger Carr and it was another lightning break from the former Connacht flyer that set O'Malley up for the first score of the night on 45 minutes.
A solo break fly-half Madigan two minutes later appeared to end the Dragons chances of victory as he raced clear from 30 yards to extend the score to 18-3 following Nacewa's successful conversion.
Dragons hopes were reignited when Tovey capitalised on a tap penalty before exchanging passes and collecting the ball ten metres out to dive over the try line and convert his own score on 57 minutes.
However Nacewa slotted a penalty and converted Carr's closing try on 77 minutes to cap off a superb display from the ex-Connacht wing.
|Leinster Rugby Score Card|
|Newport Gwent Dragons Score Card|