The Blades looked set to clinch a draw after Rovers old boy Jon Stead struck a 25th-minute equaliser shortly after Pedersen had headed the home side into an early lead.
Home debutant Stephen Warnock was then sent off in added time for a second bookable offence after clattering Derek Geary on the right wing, before Pedersen's dramatic intervention.
Blades boss Neil Warnock will hardly believe that his side headed home with nothing after a performance full of commitment and purpose which for long periods looked likely to clinch them the points.
Looking to build on the midweek win over Fulham which had left clear air between themselves and the relegation places, Warnock's men had started in suitably inspired fashion.
Bustling forward with intent, the Blades could have been three goals up inside the first 10 minutes, starting when Stead went clear only to seem surprised by no linesman's flag, and poked wide.
Moments later Stead found Rob Hulse in the box and the striker stretched to hit a weak shot which beat a diving Brad Friedel but rebounded off the base of the Rovers post.
Nick Montgomery lashed a right foot volley inches wide of target from close-range as the Blades, roared on by a raucous band of travelling fans, piled on the pressure.
Things got worse for the home side, who lost their in-form young striker Matt Derbyshire with a serious-looking injury after 15 minutes, then had Warnock booked for a bad foul.
But Rovers rode their luck and were able to snatch the lead against the run of play in the 22nd minute, when Brett Emerton cut in and crossed for Pedersen to head home at the far post.
It was a lead Rovers scarcely deserved but the visitors refused to let their heads drop and were level within three minutes following Phil Jagielka's long free-kick into the box.
Hulse flicked on towards Stead who bustled too easily past Samba on the edge of the six-yard box and struck home a right-foot shot to the delight of the travelling Blade fans behind the goal.
Stead then narrowly failed to get the decisive touch to a Tonge cross from the right as the Blades reassumed their superiority and looked dangerous each time they crossed the half-way line.
Stead was the busiest player on the pitch and he was booked by referee Marriner five minutes before the break for a poor challenge on Warnock.
Rovers enjoyed a dominant spell of their own early in the second period with David Bentley skipping around Chris Armstrong on the edge of the box and firing a deep cross which Kenny did well to flap away.
But with Stead and Hulse showing a fine understanding up front, the visitors continued to threaten going forward, and Hulse flashed an overhead kick inches wide in the 50th minute.
At the other end the Blades defence was holding firm with Chris Lucketti getting in with a magnificent interception to prevent Bentley finding the head of the lanky Samba in front of goal.
Ryan Nelsen was lucky to escape a caution from referee Marriner for his lunge on Hulse on the hour, just before Dunn came on for his second Rovers debut in place of Mokoena.
Roberts missed the chance to mark his long-awaited comeback with a goal in the 62nd minute when McCarthy laid the ball back in the box but the striker screwed his shot wide.
It was a promising spell for Rovers, for whom Pedersen came close again with a downward header from another Bentley cross, which was held well on the line by Kenny.
Warnock had a home debut to forget when he was sent off for a second bookable offence in injury time - before Pedersen stepped up to send his sensational winner past Kenny.