Felipe Contepomi's accurate right boot landed 23 points as Leinster saw off the Dragons at Donnybrook.
Leinster (14) 33
Tries: Kearney, Dempsey
Pens: Contepomi 7
Dragons (7) 14
Tries: Hinton, Luscombe
Contepomi kicked seven penalties from nine attempts and converted Girvan Dempsey's injury-time try to leave Leinster with two wins out of three.
The Irish province's other try was scored by Ireland under-19 captain Robert Kearney.
The Dragons, playing their second game in four days, had tries from Leigh Hinton and Hal Luscombe.
Hinton's try came early on after a bright start by the Dragons.
Burly Tongan Tuipulotu won the race to his own chip kick outside the home 22, flicking the bouncing ball to Luscombe and his inside pass saw Hinton dart over to score and convert.
Three Contepomi penalties pushed Leinster in front before their first fluid attack saw teenager Kearney, from 40 metres out, go past Rhys Thomas and step inside Dragons captain Kevin Morgan for a scintillating 39th-minute unconverted try.
The 51st-minute sin-binning of Dragons flanker Andrew Hall allowed Contepomi to kick Leinster 10 points in front.
But a silly deliberate offside from Kearney saw the youngster yellow-carded and that allowed the Dragons back into it.
Just past the hour, Contepomi landed his fifth penalty but that was soon cancelled out as a 71st-minute kick through from Gareth Baber squirmed away from Kearney, allowing Luscombe in for a try.
Hinton converted to put the Dragons within a converted score but the prospect of even a bonus point was soon gone as Contepomi chalked up two more penalties and Dempsey scored a try right at the end.
Leinster: Dempsey, Brown, Lewis, Contepomi, Kearney, Warner, Easterby, Corrigan, Jackman, Green, Byrnes, Gissing, Potts, Gleeson, Heaslip.
Replacements: Hickie for Brown (59), Horgan for Warner (58), O'Meara for Easterby (67), D. Blaney for Jackman (58), McCormack for Green (67), Crawford for Byrnes (76), Ronan for Gleeson (80).
Dragons: Morgan, Wyatt, Luscombe, Tuipulotu, Hinton, A. Thomas, Baber, Maddocks, Jones, R. Thomas, Gough, Charteris, Hall, Ringer, Oakley.
Replacements: Black for Maddocks (46), Brown for Jones (40), Forster for Ringer (53), Bryan for Oakley (46).
Ref: Andy Ireland (SRU).