Leinster started at pace, breaking through for their opening try after just three minutes. A move that started inside their own 22 ended with Horgan offloading for Berne to mark his first start of the league season with a try.
Full-back Nacewa added the conversion and Leinster were 10-0 ahead by the eighth minute, Nacewa doing the necessary from a penalty.
The Dragons were largely restricted to kicking in behind the Leinster defence, and a 12th minute penalty from Tovey got them on the scoreboard.
But they were caught short out wide again, in the 26th minute, when Berne used lineout possession to lob a cross-field kick over for the unchallenged Horgan to coast over for his first try of the night. Nacewa's conversion stretched Leinster's advantage to 17-3.
The Dragons should have gained the upperhand up front when Leinster captain Leo Cullen was yellow carded for taking out a support player as Scott Morgan gathered a lineout ball, near the hosts' try-line.
The Welsh region blew a three-to-one overlap on the left after a good carry from Adam Hughes, and shortly afterwards the winger was then closed down by the covering David Kearney as he fielded Tovey's punt to the corner.
Poor handling also cost them just when it looked like they might open up the Leinster defence. It remained scoreless up to half-time, leaving the Dragons with a 14-point deficit.
The opening 10 minutes of the second half saw Paul Turner's men looking lively and Tovey gave them some reward, converting the second of two penalties conceded by Leinster.
However, the hosts were able to step up a gear coming up to the hour mark, with their forwards beginning to make the hard yards.
It took a try-saving tackle from flanker Gavin Thomas and a decision from television match official Dermot Moloney to deny Leinster's Stephen Keogh as he lunged towards the whitewash from a close-in ruck.
Thomas' good work was undone when referee Stefano Penne reached for his yellow card and sent the Dragons openside to the sin-bin for a ruck offence.
Just moments later, Boss broke to the right and sent Horgan powering past Will Harries to touch down in the corner, with Nacewa's missed conversion leaving it at 22-6.
Try as they might, the Dragons were kept at arm's length and a territorially-dominant Leinster sealed the bonus point with 11 minutes to go.
Quick feet from Fergus McFadden created space for Boss to attack and a nice interchange with the impressive Eoin O'Malley led to the Ireland scrum half dotting down to the right of the posts.
Nacewa's missed conversion was immaterial as it was very much a case of job done for Joe Schmidt's understrength side.
Speaking afterwards, Shane Horgan said: "It was important to win and we're delighted to get the bonus point. We got off to a slow start but we were composed and it's good to be a part of a team that plays a nice brand of rugby.
"It's important that we keep winning and I know that all the Leinster guys who are in the Ireland camp were looking on and willing us to do well."
|Leinster Rugby Score Card|
|Newport Gwent Dragons Score Card|