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Two Jack Conan tries in the first half gave Leinster a healthy lead at half time, and Jamison Gibson-Park extended their advantage after the break.
Adam Hughes crossed for the hosts to claw back Leinster's 14-3 half-time lead before the Irish province rallied.
Richardt Strauss, James Tracy, Hayden Triggs and Luke McGrath all touched down for the visitors late on.
Munster's 30-21 defeat by the Scarlets means that Leinster leapfrog their Irish rivals to move top thanks to their demolition of Kingsley Jones' side.
The result means the Dragons, who had to play without Wales wing Ashton Hewitt due to concussion protocols in the lead up to the match, remain 10th in the table.
After a period of momentum from the hosts before the break, hopes of a Dragons comeback seemed to be extinguished in the last play of the first half, when Dorian Jones hit the crossbar with a penalty.
Despite being stunned by an influx of tries by Leinster in the second period, Matthew Screech crossed to keep the home fans entertained.
Sarel Pretorius scored a late try to take the Dragons past the 20-point mark and round off a game which saw 11 tries scored by either side.
Newport Gwent Dragons: Carl Meyer; Adam Hughes, Tyler Morgan, Jack Dixon, Pat Howard; Dorian Jones, Tavis Knoyle; Sam Hobbs, Elliot Dee, Brok Harris, Nick Crosswell, Rynard Landman, Ollie Griffiths, Nic Cudd, Lewis Evans (capt)
Replacements: Rhys Buckley, Thomas Davies, Lloyd Fairbrother, Matthew Screech, Harrison Keddie, Sarel Pretorius, Angus O'Brien, Adam Warren
Leinster: Joey Carbery; Adam Byrne, Zane Kirchner, Noel Reid, Fergus McFadden; Ross Byrne, Jamison Gibson-Park; Peter Dooley, Richardt Strauss (capt),  Michael Bent, Ross Molony, Mike McCarthy, Rhys Ruddock, Peadar Timmins, Jack Conan,
Replacements: James Tracy, Ed Byrne, Mike Ross, Hayden Triggs, Max Deegan, Luke McGrath, Cathal Marsh, Barry Daly
Referee: Marius Mitrea
Assistant referees: Claudio Blessano and Robert Price
Leinster moved top of the Pro12 table with an eight-try thrashing of Newport Gwent Dragons at Rodney Parade.