Mauro Cantoro gave the Polish side an interval lead, but a hard-working second-half display saw Mark Hughes' team deservedly take maximum points thanks to goals from Robbie Savage and David Bentley.
Rovers had the better of the opening exchanges and Bentley went close with a curling shot from 25 yards, before Morten Gamst Pedersen wasted a clear opening by volleying over from a pinpoint Brett Emerton cross.
Their early domination counted for little when they fell behind in cruel circumstances in the 28th minute.
Emerton headed clear a Wisla corner as far as Cantoro 30 yards out. The Argentinian advanced before unleashing a firmly struck shot which deflected off Tugay, leaving Brad Freidel stranded as it rolled over the line.
Savage almost provided an immediate response with a shot from the edge of the box that home goalkeeper Emilian Dolha did well to parry.
Cantoro and Jean Paulista both squandered opportunities to extend Wisla's lead ahead of the interval, before Shabani Nonda shot inches wide after Benni McCarthy had chested down Pedersen's cross to him in the penalty box.
Blackburn improved markedly after the interval and Nonda forced a good save from Dolha after jinking his way through the home defence.
They made the pressure pay in the 56th minute when Bentley curled in an inviting cross from the left wing and Savage rose to head it back across the goalkeeper and into the bottom corner.
Rovers proceeded to keep control of possession, but struggled to create chances and almost paid the price when Wisla worked a shooting chance for Paulista. However, the Brazilian was unable to find a way past Freidel.
Buoyed by the escape, Hughes' men went in search of the winner they deserved and found it in the 89th minute.
Substitute Jason Roberts raced through the home defence, only to see his shot blocked by Dolha, who also parried McCarthy's follow up. But it was third time lucky when the ball fell to Bentley, who steered it home from a narrow angle.