An early try from Ireland international Dave Kearney gave Leinster the upper hand before scores from Scott Penny and Scott Fardy, with Dragons reduced to 14 men, sent them 19-3 clear at the break.
Kearney wrapped up the bonus point before Dragons hit back with a well-worked try from scrum half Rhodri Williams.
But further scores from Caelan Doris, Hugo Keenan and Jimmy O’Brien (2) sent Leinster past the half century on a difficult night for Bernard Jackman’s men.
Dragons made one change to the starting line-up with Aaron Wainwright coming into the side while Wales internationals Cory Hill, Ross Moriarty and Elliot Dee were named on the bench.
Ollie Griffiths and Rynard Landman smashed up the middle as Dragons looked to leave an early impression before a loose floated pass saw the Irish province strike.
The ball was repeatedly punched up the middle before fly half Ross Byrne cleverly picked out Kearney on the wing with a low kick and the Ireland ace collected and slid over.
The Leinster pressure was building as centre Conor O’Brien swatted off a tackle to break and, after Kearney almost made it to the corner with a powerful burst, the visiting forwards looked to bulldoze over.
The try was chalked off by the TMO but a penalty was still given and, with Lewis Evans yellow carded, the second try arrived as flanker Penny crashed over.
Home fly half Jason Tovey reduced the lead with a well-struck penalty, after two quick penalties against Leinster at the breakdown.
Leinster wing Adam Byrne was denied by a fine last ditch tackle but captain Fardy sent over after a long pass picked him out for an unopposed run to the corner.
Dragons enjoyed their best spell of the match before the break as Williams kicked in behind to force Leinster into a lineout ten metres out.
The set piece was then stolen and the home pack surged for the line, with back row Harri Keddie held up. Dragons then went again from a five-metre scrum but a knock on halted momentum.
Dragons made two half-time changes, as Hill and Brown were introduced. But they could do little as a carbon copy of the first try saw Byrne pick out Kearney to wrap up the bonus point.
Back came Dragons as a break up the middle allowed Keddie to offload for Williams who beat three men in a foot race to the slide over. Tovey added the extras to reduce the lead to 26-10.
Adam Byrne saw a third Leinster try chalked off by the TMO in the match, for a knock on as he looked to ground a low grubber kick from O’Brien.
But moments later Number Eight Doris was over, after a neat flat pass close to the line, before Hugo Keenan and Jimmy O’Brien (2) added further scores as the visitors pulled further clear in the final quarter.
07m Kearney t R Byrne c 0-7
12m Penny t R Byrne c 0-14
19m Tovey p 3-14
23m Fardy t 3-19
43m Kearney t R Byrne c 3-26
46m R Williams t Tovey c 10-26
55m Doris t R Byrne c 10-33
62m Keenan t R Byrne c 10-40
66m B Byrne t 10-45
68m J O’Brien t Frawley c 10-52
79m J O’Brien t Frawley c 10-59
Referee: Lloyd Linton (SRU)