Nene Macdonald, Chris Atkin and Deon Cross all scored in the final 16 minutes for the Red Devils, while Marc Sneyd kicked four goals from as many attempts to inflict the first defeat of the season on Paul Wellens' men.
It was a win greeted with scenes of wild celebration from the travelling Salford fans, who had seen their team lose 41 times in St Helens before breaking that sequence.
St Helens centre Mark Percival scored a try and kicked a goal before being sent off in the 45th minute after a late hit on Salford prop Jack Ormondroyd when Saints were leading 14-6.
But the 12 men actually added to their lead, with Lewis Dodd scoring his second try with 21 minutes left and converting it himself to extend the advantage to 20-6.
But Salford rallied with those late scores from Macdonald, Atkin and Cross and turned things around.
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