Rovers, playing for the first time since being taken over by Indian company Venky's, took the lead in stoppage time at the end of the opening period at Ewood Park thanks to Pedersen's delightful looping free-kick.
The Norwegian then struck again midway through the second half to wrap up a comfortable victory for Sam Allardyce's side.
Venkateshwara and Balaji Rao, the directors of Venky's, came on to the pitch to greet Blackburn's fans before kick-off and received warm applause.
Once things got under way Rovers' players seemed eager to please the new owners as well, with Jason Roberts sending a dangerous ball into the box in the opening few minutes that was cleared away.
The home side then won a free-kick just outside the area which was laid to Christopher Samba, only for the captain to skew his effort wide.
Villa went on the attack almost immediately after, though, and Paul Robinson did well to save Stewart Downing's low drive with his feet.
The visitors went close again when Barry Bannan drilled wide and Robinson was called into action once more around the quarter-hour mark, pushing Ashley Young's shot away after the England winger had tied Michel Salgado in knots.
Blackburn regained possession and former Rovers defender Stephen Warnock made a great intervention to take the ball away from Roberts as he bore down on goal.
Gael Givet then sliced an attempt over the bar after a failed clearance by Villa.
Allardyce's team were starting to impose themselves a little more and Pedersen's dead-ball deliveries began to cause problems, Roberts meeting one free-kick but was unable to keep his header down.
El-Hadji Diouf got his header closer to the target four minutes before the break but Brad Friedel claimed it and Stephen Ireland nodded over at the other end.
Rovers then snatched the lead just before the interval through another Pedersen free-kick, the midfielder curling a strike perfectly just over Friedel and in.
Having brought on Pascal Chimbonda for Givet at half-time, Rovers found themselves almost immediately under pressure after the restart as Ashley Young had one shot palmed away by Robinson and then saw his header come back off the crossbar.
Play switched though, and Roberts lashed one wild effort high and wide before picking out Phil Jones, who beat one man but could only fire into Friedel's arms.
Pedersen unleashed another dangerous free-kick which several of his team-mates were just unable to get on the end of and then Roberts put Diouf through, but Richard Dunne did just enough to ensure Friedel could deal with the Senegalese forward's shot.
The hosts appeared to be threatening another goal and in the 66th minute it duly arrived, Pedersen again providing the finish after getting his foot to Ryan Nelsen's drive following a scramble at a corner.
Villa boss Gerard Houllier responded by bringing on Robert Pires in place of Ireland, the French veteran making his first Premier League appearance since 2006.
Diouf had a chance to make it 3-0 but headed over and Robinson did well again to deny Downing.
Nathan Delfouneso then came on for the ineffective Gabriel Agbonlahor, while Allardyce withdrew Pedersen, sending on Herold Goulon for his debut.
Delfouneso was unable to get any direction on a header soon after and Ashley Young protested that Jones had handled in the box.
His appeal was waved away by referee Michael Oliver, though, and Rovers hung on to secure the three points.