Percy Montgomery, a former Rodney Parade hero put over one of two early penalties from 22 metres and, after 28 minutes, Montgomery's quick hands put in Jean-Philippe Grandclaude to touchdown for a score that Montgomery converted.
A second Montgomery penalty on the resumption eased Perpignan into a 13-0 lead and that seemed to be that, given the scoring chances the Dragons had to that point.
The Welsh Region found some fighting spirit but still could not get any points on the board by the hour mark. Centre Phil Dollman could not ground the ball when put under the posts by Sweeney.
As the Dragons pack rumbled around the fringes of a rolling maul they could not quite find the gaps to go over. Replacement scrum half Andy Williams put through a dangerous grubber kick that Perpignan just managed to get safe.
The Dragons' afternoon was summed up as David Marty intercepted a lazy pass on halfway by flanker Joe Bearman to stretch his legs and go over from 50 metres.
With the final move of the match Perpignan rounded things off with a third try as winger Adrian Plante went over in the corner for Montgomery to convert.
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