The Lilywhites had previously only won once in eight league games this season, but they swept aside a poor Saints side at Deepdale to ease the pressure on Simpson.
He fumed afterwards: "It's difficult to ignore all the rubbish that is thrown at you.
"You do start to question every little thing that you do. I think everyone knows what we have to put up with, but this result and performance had been coming.
"The players did everything that we asked of them and they showed some character to come out after half-time and score four goals."