But it was far from plain sailing for the the Dublin side, who had to fight theri way back from 13-3 down with second tries from Bernard Jackman and Rocky Elsom.
Replacement fly-half David Holwell, who has rejoined Leinster on a temporary contract, chipped in with a late penalty, as did centre Fergus McFadden who did his prospects no end of good with an impressive display.
But the match began with the visitors adapting well to the wintry conditions, and the Dragons were quickly 6-0 ahead thanks to two James Arlidge penalties.
With Jonathan Sexton receiving medical attention, McFadden booted the hosts’ first points after 19 minutes, but the Dragons pulled ten points clear when second row Hoani MacDonald grabbed an intercept try.
The Junior All Black swooped on a loose pass from Sexton to gallop over close to the posts, just after Arlidge had missed a penalty.
Leinster responded almost immediately with flanker Sean O’Brien coming in on a great angle into the Dragons’ 22 and he handed off Arlidge to complete a fine individual score.
Sexton converted and while the Dragons lost MacDonald to the sin-bin for his hauling down of Devin Toner at a lineout, their lead still stood at 13-10 at the break.
With better continuity and a solid platform up front, Leinster began to turn the screw in the third quarter.
Sexton levelled matters with a well-struck penalty and after repeated darts at the Dragons line, hooker Jackman put Leinster out of their misery by scoring on the hour mark.
The try went unconverted as Sexton’s conversion bounced off the left hand post and had Arlidge bisected the uprights soon after at the other end, the pressure would have mounted on Leinster.
As it was, the hosts had enough class on show to see out a win which moves them up to fourth in the table.
Holwell kicked the second of his two penalty attempts, McFadden also landed a penalty and then, in injury-time, after a fantastic raid forward from Girvan Dempsey, Holwell showed great hands to send Elsom tearing over at the right corner to add some gloss to the scoreline.
And although Leinster managed to recover from an early 13-3 deficit, the night was somewhat soured by a shoulder injury to Brian O’Driscoll.
With ten players currently out injured, Michael Cheika can ill-afford to lose a player of O’Driscoll’s calibre.
