Jordan Rhodes put the visitors ahead from the spot before a strike from Jermaine Johnson and Leroy Lita's penalty gave Wednesday the lead at the break.
Scott Dann levelled for Rovers after 71 minutes, before Johnson put his side back in front seven minutes later with a second impressive strike.
Johnson's moments of individual brilliance were the highlights of a tense affair in South Yorkshire, although the win moved Wednesday three points clear of the drop zone.
Wednesday forced a succession of early corners but it was the visitors who created the first chance with David Dunn's accurate cross forcing a scrambling Chris Kirkland to deflect the ball to safety. After 12 minutes Kirkland was scrambling again, but this time he was caught out.
Miguel Llera was comfortably beaten for pace by Rhodes who got on the end of a long ball over the top. Although Kirkland stopped the Scottish striker, the ball fell to Dunn who went down under the stopper's challenge. Rhodes sent Kirkland the wrong way for his 25th goal of the season.
Within eight minutes Wednesday were level. A ball into the box fell kindly for Johnson, who cut inside and with Rovers defenders slow to react, fired hard and low into the corner of the net.
Things went from bad to worse for Blackburn in the 35th minute when Reda Johnson was bundled over as Grzegorz Sandomierski claimed a cross into the box. Lita tucked away the spot-kick for his fourth Wednesday goal.
Blackburn levelled things up in the 71st minute when Josh King's inswinging cross found Dann who got goal-side of Llera to head home.
Their lead was not to last long. Johnson broke forward and with Blackburn again retreating, fired an unstoppable piledriver into the bottom corner.