Two years ago, Wrexham and Stockport were non-League rivals, but on this occasion, Wrexham struggled to threaten the Stockport goal. The hosts put on a dominant performance and emerged as deserving winners.
After a well-matched opening to the game, Barry's spectacular strike put County ahead. Ollie Norwood's drive was blocked and when the ball came to Barry he turned and unleashed an inch-perfect finish into the top corner.
Stockport started to turn the screw after that but could not find a second goal, with Will Collar denied by a deflection that sent the ball wide after he had picked the pocket of defender Tom O'Connor.
Wrexham were grateful to goalkeeper Callum Burton for a terrific double save 10 minutes before the break. Barry's whipped cross was headed goalwards by Collar and Burton got a vital hand to the ball at full stretch, recovering quickly to block Fraser Horsfall's follow-up.
TrendingWith the visitors under mounting pressure, a clearing header fell for Norwood and his audacious first-time volley from 25 yards narrowly cleared the crossbar.
Stockport continued to see chances go begging after the break, with Ethan Pye heading over and Barry and Kyle Wootton both frustrated by excellent saves from Burton.
The Dragons had a late chance to snatch a point but when James McClean picked out the unmarked Elliot Lee, he headed wide.