Comeback man Dave Halley earned Bradford their first win of the engage Super League season with the last play of the match in a dramatic clash in Perpignan.
The winger had been recalled from a loan spell at Wakefield earlier this week and returned to score an amazing 80th-minute try to ease the pressure on Bulls boss Steve McNamara.
Now it is Catalans coach Kevin Walters who is under the cosh after his side slipped to their fifth defeat of the year.
The gutted hosts thought they had ended the rut when Jean-Philippe Baile's 67th-minute try gave them the lead for the first time since the fourth minute.
Catalans had already had three efforts turned down by the video referee after powering past the visitors in the second half.
But Bradford clung on and Terry Newton's 74th-minute touchdown brought them back to just two points behind.
Paul Sykes missed the easy conversion but slotted a 77th-minute penalty to level. Bradford then lined up for a drop goal in the dying seconds but, as the Catalans defence pressured, Sykes handed on to Ben Jeffries who darted clear and sent Halley over.
It means Bradford remain the only side to boast a 100 per cent record in Perpignan.
Thomas Bosc put the hosts ahead with a fourth-minute penalty but Bradford started strongest and soon built up a deserved 12-2 lead.
Jeffries' perfectly-weighted chip landed in Steve Menzies' grasp for a simple walk-in and soon after Semi Tadulala hit a gap before producing a great step to leave Clint Greenshields rooted.
Paul Deacon improved both scores and Bradford were full of confidence.
A couple of cheap penalties handed Catalans some much-needed field position and from that winger Thomas Duport hit back in the corner on 18 minutes.
Bosc improved but a Deacon penalty kept the visitors out in front and they extended that lead when Rikki Sheriffe grabbed his third try in as many games with a fine score.
Menzies started the movement deep inside his own half with Sykes bumping his way clear and Deacon supporting the break before Sheriffe finished.
Deacon could not convert and it looked like it might prove costly as Catalans finally came to life with two tries in three minutes just before the break.
New skipper Greg Bird capitalised when Michael Platt dropped a Bosc bomb and then Olivier Elima powered over from close range with Bosc converting twice to make it 18-18 at the interval.
Catalans - with Bird immense against the side he originally signed for before hitting visa trouble - bossed the second half and could not believe it when each 'try' was ruled out.
They thought Baile had got them only their second win but then Halley popped up with his fifth try of the season, having hit four in his loan spell at Wakefield.