The victory was also a third in four games in charge for John Cartwright.
The former Hull FC head coach was appointed until the end of the season last month, but reports earlier in the week suggest he could extend that to the end of 2027.
His charges made a great start when Lipowicz crossed after six minutes, but Sutton quickly levelled things up.
Allen crashed over for the hosts after a Bradford error gave them good field position, but once again the Bulls quickly got a try of their own as Ryan dived over for his 10th of the year.
Scores from Bousquet and Faataape gave Catalans a 12-point lead at the break, but Wynne snaffled a loose ball and finished well in the opening minutes of the second half to get the Bulls back within eight.
The visitors then fumbled the ball on the restart, though, and Leeming punished them.
Guy Armitage and Ryan had tries ruled out as Bradford fought gamely before Aekins gathered Wynne’s kick to once more get them within eight points.
Once again, though, the Bulls could not build on their try, and Staines punished more lax defending to put the game beyond them and leave Wynne’s late score just a consolation.
The Dragons’ improved form will be tested with a trip to second-placed Warrington on Thursday, while Bradford will look to return to winning ways at home to St Helens next Saturday.
Catalans: Staines, Makinson, Aispuro-Bichet, Faataape, Cotric, Sexton, Dodd, Allen, Leeming, Navarette, Maria, Lipowicz, Bousquet.
Interchanges: Satae, Condon, Wilson, Laguerre.
Bradford: Aekins, Wynne, Armitage, Ryan, Nikorima, Atkin, Sutton, Ackers, Doro, Russell, Blake, Steinwede, Mellor.
Interchanges: Scurr, Gardiner, Peposhi, Dean.
Referee: Matty Lynn.
