After Dane Carlaw's opener, full-back Clint Greenshields touched down twice, either side of Casey McGuire's effort.
But the Dragons were not to be denied, with Gregory Mounis, Clint Greenshields and Murphy (2) completing the rout.
But after trading tries, Greenshields towered above full-back Matt Sing to take in Bosc's kick and score under the posts.
But three second-half tries in 19 minutes through Clint Greenshields, Setamaita Sa and Sebastien Rougin saw the Dragons turn it round.
Greenshields ran over this third try of the game with 10 minutes remaining which Bosc converted to open up a sizeable advantage.
Cohen and his team went through various iterations to improve their GreenShields.
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Tom Briscoe responded for Hull before Clint Greenshields clinched victory late on.
Barrett then made it two tries in three minutes following a wonderful jinking run which saw the Australian dummy his way past Greenshields.
But after the break, a brilliant running move involving Bosc, Clinton Greenshields and Justin Murphy gave McGuire the chance to score out wide.
BBC: SPORT | Rugby League | My Club | Catalans Dragons 30-22 Leeds
One of them is Jonny Cohen, a high school senior, celebrated green entrepreneur, Ashoka Youth Venture award winner, and creator of GreenShields.
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But the French drew level thanks to winger Duport's try midway through the first half after some trickery from debutant full-back Clint Greenshields.
But a poor Stefan Ratchford chip kick enabled the Dragons to race the full length of the field for Greenshields to cross in the corner.
Bosc's clever hanging kick allowed Greenshields to touch down and then a teasing grubber from Bosc saw McGuire dive full length to ground the ball.
The Dragons took a 10-4 half-time lead thanks to tries from Aaron Gorrell and Keith Greenshields, with Pat Richards adding a touch down for the visitors.
Gorrell opened the scoring in the 17th minute when he powered over from dummy-half before feeding Greenshields 10 minutes later for the French side's second score.
Catalans had a Clint Greenshields try ruled out for an obvious offside before Mogg saw yellow after holding onto Ashton in the tackle as Wigan attacked.
The Dragons' best try came shortly before the break as some fine passing down the right channel ripped Saints apart, allowing Greenshields to go over for his second try.
Sinfield kicked down the length of the field to Scott Donald who gathered but was just caught by Clint Greenshields, but the ball then went wide for Jones-Buchanan to score.
BBC: SPORT | Rugby League | My Club | Catalans Dragons 30-22 Leeds
Korkidas pulled a try back for Castleford but Clint Greenshields touched down on the stroke of half-time and Bosc landed a penalty on 50 minutes to extend his side's lead to 32-18.
Richards confidently kicked the extras but again the Dragons refused to lie down and a try from Greenshields brought them back into the game as Bosc again showed his prowess with the boot.
Murphy followed up John Wilson's kick to the corner to complete his hat-trick, Mounis finished off a slick handling move, and Adam Mogg sent Greenshields sprinting 40 metres for his 18th try of the season.
Gale missed a straightforward conversion but atoned when, after Dorn had outjumped Clint Greenshields to claim a towering kick, he flicked the ball up for Gale, who not only scored again but this time made no mistake with the extras.
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