Jordan Rhodes put the visitors ahead from the spot but the home side hit the front thanks to a Jermaine Johnson strike and a Leroy Lita penalty nine minutes before the break.
Scott Dann levelled for Rovers after 71 minutes, before Johnson put his side back in front seven minutes later with his 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.
Blackburn came into the contest without a win since beating Arsenal in the FA Cup in February, while inconsistent Wednesday were in decent form with their only defeat in four games coming at Cardiff.
Dave Jones made four changes from the side which drew with Bristol City, with loan duo Seyi Olofinjana and Stuart Holden back after recovering from knocks, Lewis Buxton from suspension, while Lita was preferred to Steve Howard up front.
After they were beaten 3-0 at Cardiff, visiting caretaker boss Gary Bowyer made six changes with Grzegorz Sandomierski, Lee Williamson, Jason Lowe, Cameron Stewart, Rhodes and David Dunn all coming in.
Wednesday forced a succession of early corners but it was the visitors who created the first chance with 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.
The hosts should have taken the lead when Lita's dummy played in Jeremy Helan and with Blackburn ball-watching he turned and screwed his shot over.
Blackburn were dropping deeper and deeper and after 35 minutes found themselves in trouble.
Reda Johnson was bundled over as Sandomierski claimed a cross into the box and linesman Matthew Buonassisi immediately flagged for a penalty.
There was little protest apart from the goalkeeper and Lita tucked away the spot-kick for his fourth Wednesday goal.
The on-loan Swansea man could have put his side two goals ahead when he was played through, but Sandomierski pushed his effort away from goal.
After a lacklustre opening 10 minutes of the second half, Bowyer brought on Kazim-Richards for Stewart, while Kieran Lee replaced Holden.
Josh King came on for Lee Williamson as Blackburn again tried to increase their attacking options, but with little creativity and Wednesday reasonably strong at the back, chances were hard to come by.
With Wednesday insisting on playing long balls forward, Howard for Lita was a logical substitution after 70 minutes.
However it was at the other end where Wednesday were starting to have trouble and seconds later Blackburn were level, 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.
Blackburn could not respond again and their winless run stretched to 11 matches, while Wednesday eased their relegation fears - at least until Tuesday when they face Millwall at The Den.