It was the Norwegian winger's fifth goal in his last ten appearances and one which earns Blackburn the East Lancashire bragging rights.
However, Burnley were stubborn opponents and you had to feel a little sorry for them in the end.
Rovers struggled to find anything like their best form although they did enjoy the lion's share of first-half possession and took a deserved if rather fortunate lead in the 32nd minute.
Pedersen and Lucas Neill had already gone close for the home side before Tugay silenced the visiting fans with a shot which caught a wicked deflection off Micah Hyde to wrong-foot Jensen.
Pedersen went close from distance soon after before Burnley pulled themselves level with a real goal of the season contender just before half-time.
There appeared little danger when a clearance bounced kindly for Hyde some 20 yards out. The midfielder swung his foot at the opportunity and the ball dipped over Brad Friedel for a spectacular equaliser.
Blackburn skipper Ryan Nelsen twice went close to giving his side the lead in the opening minutes of the second half.
His firm header from a Pedersen corner brought a brilliant reflex save from Jensen before the defender was just inches too high with another acrobatic header.
Blackburn held the upper hand in terms of possession but struggled to break down a Burnley side with a proven game-plan and a resilient attitude.
But Burnley hearts were broken just when it looked like the tie was heading for extra-time.
Pedersen again emerged as Rovers' golden boy and it was his name being chanted by joyous supporters at the end.