Defending champions Leeds suffered a third Super League defeat and remain bottom of the table after Catalans hold on for their first win of 2016.
Dave Taylor gave Dragons the lead only for Kallum Watkins to respond. Richie Myler's score helped edge Catalans 12-8 ahead at the break, with quick tries from Krisnan Inu and Tony Gigot putting the hosts in control.
While Liam Sutcliffe, Ryan Hall, Ash Handley and Watkins went in for Leeds, Taylor's second score ensured victory. Leeds' defeat in France is their fourth in all competitions this season and came six days after their 34-8 World Club Challenge defeat by North Queensland Cowboys.
With seven key members of their squad out injured - including captain Danny McGuire and talismanic winger Tom Briscoe - and Mitch Garbutt banned for two matches, Rhinos got off to the worst possible start when Todd Carney's inside pass found Taylor, who powered over the line. Pat Richards converted to open an early 6-0 lead.
But an awful error from Tony Gigot, who lost the ball forward in the in-goal area, allowed Watkins to touch down and Jordan Lilley levelled from the tee.
Former Australian Kangaroos international prop Willie Mason came off the bench with the scores level to make his Catalans debut and Super League return after a brief stint in the competition with Hull KR in 2011.
Dragons, who were also without a win in their opening two games, regained the lead as new signing Jodie Broughton's clever inside kick was collected by fellow new boy Myler.
Lilley slotted a penalty before the break to reduce the arrears, but Leeds were caught cold within seconds of the restart as Inu powered through the Rhinos defence and Gigot then atoned for his earlier error as Brian McDermott's Rhinos switched off.
But last season's treble winners then created a try out of nothing as Watkins and Mitch Achurch showed their class for Sutcliffe to finish, before Hall stormed over to reduce the gap to four points.
And, as the rain lashed down in Perpignan, Taylor once again charged through three Leeds defenders to score and put Catalans in command. Rhinos set up a tense finish, scoring two length-of-the-field tries through Handley and Watkins, but Catalans closed out the game to move up to eighth in the table.