Brian Laws' Wednesday side snatched the lead with just two minutes gone with on-loan Derby striker Luke Varney finding the target before the promotion favourites hit back thanks to a Darren Purse own goal and a quality finish from Frenchman Jeremie Aliadiere.
But it was Johnson who sealed the win five minutes from time after showing the skills that have made him a target for several Premier League side.
Wednesday swept ahead in spectacular fashion when midfielder Darren Potter threaded the ball to Varney, who weaved past Seb Hines and lashed in a left-foot strike off the underside of the bar.
Marcus Tudgay drilled in a a low strike from 20 yards which was scooped up on the line by Danny Coyne, before Marvin Emnes was foiled by Lee Grant after the striker had cut inside from the left flank.
Middlesbrough were back on level terms in the 19th minute with dangerman Johnson carving out the goal as he whipped in a vicious cross which came off Purse's head and bounced into the far corner.
Wednesday escaped on the stroke of half-time after Potter's head caused problems in the Wednesday area.
Middlesbrough snatched the lead in the 50th minute with a sweeping move down field. Emnes unselfishly passed inside to Aliadiere, who lashed an angled left-foot strike beyond Grant.
Johnson saw his fierce strike pushed away by the Wednesday keeper, before Middlesbrough almost grabbed a third.
Hines stretched to meet a Gary O'Neil corner but his downward header at the far post was palmed away in spectacular fashion by by Grant.
Johnson struck in the 85th minute after running onto O'Neil's long pass before twisting inside to hammer a low right-foot winning strike into the far corner of the net.