The Wales Under-20s star landed six penalties while fly-half Steffan Jones kicked a hat-trick of drop goals to steer the Dragons home.
Prop Phil Price crossed on the stroke of half-time and despite conceding two tries, the Dragons capitalised on Scottish indiscipline to clinch a handsome victory.
The win lifts the Dragons two places in the RaboDirect Pro12 table.
However it looked to be a different story when they got off to the worst possible start when Lydiate had to be helped off the pitch inside two minutes and Edinburgh grabbed the opening score when wing Tom Brown finished a sweeping attack.
Prydie chipped away at the deficit and handed the Dragons the lead on 25 minutes with a third penalty while Edinburgh’s young fly-half missed twice.
Prydie stretched the lead with a fourth kick despite hooker Steve Jones being sent to the sin bin for a professional foul.
And the Dragons took the game in their claws in a ten-minute purple patch either side of half-time that brought 13 points and saw Edinburgh reduced to 13 men.
Edinburgh skipper Sean Cox was shown a yellow card for a foul on Ian Nimmo.
Steffan Jones set up and attacking lineout with his kick up field from the resulting penalty.
Prop Price was forced to take the throw, with hooker Jones still in the sin bin, but his quick-thinking caught Edinburgh off-guard.
The front-row’s throw was immediately returned by Nimmo and Price scurried over from 20 yards out to touch down in the corner.
Prydie missed the conversion with the last kick of the first half but opened a 20-7 lead two minutes after the break when Edinburgh flanker Ross Rennie joined Cox in the sin bin.
Toby Faletau showed his defensive qualities with a try-saving tackle on Nick De Luca when the Scotland international centre looked destined to score.
Edinburgh’s woe was compounded when fly-half Jones kicked a drop goal in 48th minute for a 23-7 lead.
Visser clawed back a second try for the visitors but they could do little to stop the Dragons’ twin boots of Jones and Prydie who kicked the home side to a precious win.
