Catalans started strongly, racing to a 10-0 lead thanks to two tries to Broughton.
Saints hit back with a try from Theo Fages. Broughton then crossed for his third on 33 minutes to make it 14-6.
But right before half-time the home team responded through Luke Walsh, the little halfback smartly chipping and chasing to score.
He converted his own try to take the score to 12-14 at the break.
The game was in the balance but in the second half the Dragons stepped it up.
Broughton crossed for his fourth to finish Saints off.
Catalans are now equal top of Super League with Warrington on 16 points.
The home defeat was St Helens third at Langtree Park in a row.