Will Boyle scored the decisive goal as Shrewsbury made it five wins in a row, at Salford, on a night when Joe Hart filled in as the visitors' goalkeeper coach.
Former England and Manchester City goalkeeper Hart, who started his career in Salop, was helping his old club out for the game.
And he saw Gavin Cowan's side overturn a half-time deficit to continue their impressive form.
Boyle's strike condemned Salford to a fifth straight defeat in all competitions, though they started brightly as Ossama Ashley and Jorge Grant both went close.
The home side took a fortuitous lead in the second minute of first-half stoppage time when Matthew Cox pushed a mis-hit Ryan Graydon volley against Luca Hoole and the ball rebounded into the net for an own goal.
Shrewsbury levelled six minutes after the break when Tom Sang picked out the bottom corner from the edge of the box after Josh Ruffels' initial shot had been cleared off the line.
Josh Austerfield rattled the Shrews' bar with a powerful header before team-mate Ben Woodburn had a volley cleared off the line.
But Karl Robinson's side would be made to rue those missed chances after 76 minutes when Boyle fired into the bottom corner to seal victory.
Report supplied by PA Media
Karl Robinson: 'I have to take the blame'
Gavin Cowan: 'Really proud of the players yet again'
