Fryatt broke the deadlock with his 15th goal of the season in the 86th minute before being joined on the scoresheet by Kris Taylor and Mark Wright.
Fryatt's classy goal capped a perfect day for the England youth international who collected Walsall's player of the year award before the game.
The goals also spared the blushes of Darren Wrack who missed four golden chances - including a 17th minute penalty when he failed to even hit the target.
Stockport had not won an away game since February and only picked up three victories on the road all season and, apart from a brief spell in the second half, they never looked like improving on that dismal statistic.
Walsall threatened early when Simon Osborn and Michael Standing went close before surviving a scare of their own after Danny Jackman's ninth minute cross-shot hit the bar.
But Walsall should really have broken the deadlock eight minutes later only for Wrack to fluff his big chance.
Julian Joachim, Walsall's on-loan striker, surged into the penalty area and was hauled down by a rash challenge from central defender Ludovic Dje.
Referee Kevin Wright had no hesitation in pointing to the spot but Wrack dragged his right-foot shot wide.
Wrack then let off Stockport for a second time eight minutes before half time when he failed to convert a left-wing cross from debutant full-back Jon Harkness.
Wrack's frustrations showed no sign of abating in the second-half.
He hit the post in the 61st minute with a curling shot after being picked out by a pass from substitute Fryatt before missing again from close range 60 seconds later after latching on to a centre from Wright.
Wrack's failings could have been punished but for a fantastic challenge by Walsall defender Craig Pead who bravely blocked a shot from Adam Le Fondre in what was a rare Stockport attack after 69 minutes.
That moment of promise inspired Stockport and it needed a smart 72nd minute save by Walsall goalkeeper Andy Oakes to prevent Damien Allen firing County ahead.
But the game was turned on its head in the 86th minute when Fryatt showed Dje a clean pair of heels and raced clear to drill a low shot past Neil Cutler.
Three minutes later a 20-yard free-kick from Taylor crashed off the bar and was adjudged to have crossed the line.
Wright then completed Walsall's impressive late flurry by steering a cross from Joachim into an empty net from 10 yards.