It was not all good news for the victors, though, as Wales flanker Dan Lydiate was helped off the pitch with an ankle injury within the first two minutes.
Prop Phil Price scored the Dragons' only try but Prydie's boot plus three drop goals from fly-half Steffan Jones put the hosts in the comfort zone.
Edinburgh scored tries through wing Tom Brown and centre Tim Visser, with fly-half Harry Leonard adding a conversion.
The Welsh outfit have slipped to the wrong end of the table after defeats to arch-rivals Cardiff Blues and then to Munster in Limerick last weekend.
Edinburgh, meanwhile, were looking to bounce back from their own loss in Ireland last week where they went down 22-16 at Leinster.
And, after a hesitant start, the visitors grabbed the first score of the match when a sweeping movement through the half-backs to midfield saw Visser throw a long ball out to the right for Brown to capture and get the touchdown amid heavy defence.
But the Scottish side lost their way and, for the rest of the first half-hour, did not threaten the home line. The Dragons ruled the line-out as Edinburgh hooker Andy Titterrell, the former England international, lost his direction. It did not help Edinburgh's cause either that they repeatedly gave away penalties in the range of Prydie.
The ex-Wales international had mediocre displays with the boot against the Blues and Munster but was spot on three times before the break from distance as the Dragons established a 9-7 lead.
Leonard had two chances of putting Edinburgh back in front with penalties from out wide, but missed them both.
Edinburgh had a five-minute advantage when home hooker Steve Jones was sent to the sin-bin for an offside at a ruck which seemed easily avoidable.
Visiting captain Sean Cox also found himself off the field for 10 minutes soon after, though, when he was deemed to have up-ended home lock Ian Nimmo, although it appeared referee John Lacey had the wrong man with Robert McAlpine in the thick of the action.
The disruption looked to have upset the Scottish team, who swiftly surrendered a try. The Dragons found themselves just outside the Edinburgh 22 but quick thinking by Price, taking the throw-in while Jones was off the field, found Nimmo who quickly threw the ball back to the prop. And, with a nippy turn of pace, Price darted 30 metres to the line to the roars of the home crowd and to the delight of his team-mates to give the Dragons a 17-7 half-time cushion.
Edinburgh did themselves no favours again after the break when they gave away a penalty that Prydie gladly converted from 25 metres and, after Ross Rennie had been sent to the sin-bin for an offside offence, Steffan Jones came into his own.
He landed three drop-goals which, with more Prydie penalties, was more than enough to finish off the Scots.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.