Stephen Warnock was dismissed on his home debut for Mark Hughes' side late in the game after picking up his second yellow card.
Fresh from a 2-0 win over Fulham on Tuesday night, the visitors started much the better of the two sides. On six minutes, the Rovers defence came rushing out trying to play off-side from a Sheffield United free-kick, but Stead was left free in the centre and his stabbed effort goalwards drifted inches wide of Brad Friedel's left-hand post.
Two minutes later, Stead's whipped ball in from the right caused havoc for the Rovers defence, Stephen Quinn centred for Rob Hulse, whose deflected shot struck the foot of the same post and was cleared to safety.
On ten minutes, a corner from the right was kept alive at the back post by Chris Lucketti, but somehow the unmarked Nick Montgomery volleyed wide with the goal at his mercy.
Rovers were dealt a cruel blow when Matt Derbyshire - called up to the England Under-21s just 48 hours earlier - pulled up on the left flank after 15 minutes and was replaced by Jason Roberts. And the former Wigan striker, making his first appearance since breaking a bone in his foot in late October, almost made a dream return.
But after latching on to Pedersen's through ball, he curled a right-foot shot wide of Paddy Kenny's goal from outside the box.
But on the midway point of the half, just two minutes later, Rovers did take the lead against the run of play. After some good work down the right by Brett Emerton, the Australian supplied an excellent deep cross to the back post, where Pedersen rose above his marker to power a header past Kenny into the roof of the net.
But Rovers could only hold their lead for just three minutes, as the Blades stuck back with their next attack. A long free-kick from the half-way line was flicked on by Hulse and Stead got in front of Christopher Samba to fire past Friedel from close range.
Rovers responded well however and ought to have regained their lead on 33 minutes. Pedersen was played clean through with a ball over the top, but with time and space to pick his corner, the Norwegian dragged his right-foot shot agonisingly wide of the mark.
The home side continued where they left off after the break and almost scored a wonder goal. Three minutes into the second half David Bentley kept the ball in play on the right touchline with a magnificent flick, then turned Chris Armstrong inside out before forcing a fine diving save from Kenny with a right-foot shot.
United responded well and could have netted at the other end just four minutes later. A corner from the left was headed forward by Lucketti and Hulse's overhead kick flashed inches wide of the post.
David Dunn was introduced for his second Rovers debut shortly after and lifted by his return, the home side began to play some decent stuff. On 62 minutes, Benni McCarthy and Roberts played a neat one-two, before the latter fired just wide.
As the clock ticked down, a trademark Pedersen free-kick was well saved by Kenny, before Warnock was shown his second yellow card of the game and sent for an early bath.
But as the game entered the third and final minute of stoppage time, Dunn's surging run was brought to a halt and up stepped Pedersen to curl a left-foot free-kick over the wall for his sixth goal in his last seven games.