The Welsh region were right in the game until the second period when Leinster stretched away scoring three tries.
The hosts looked like a different side to the one that was comfortably beaten by the Ospreys last weekend, but for their early pressure their reward was only two first-half penalties from Isa Nacewa.
By half-time in Cork last Saturday the Dragons had a mountain to climb but it was a different story in Dublin, with a Jason Tovey penalty keeping them in touch at half-time with the scores 6 v 3 at the break.
After the interval Brendan Macken and then Ian Madigan crossed for tries in quick succession for Leinster, after a promising spell from the visitors.
Nacewa then added another penalty taking his tally to 11.
The Dragons were commended for their never-say-die attitude against Munster last Saturday and that continued as they forced their way back into the game with a try from Tovey.
But two further penalties from the impressive Nacewa and then a third try from Fionn Carr sealed the game for Leinster and the Dragons’ hunt for a first victory in Ireland in three years continues.
