The Blackburn midfielder curled a superb 34th-minute free-kick past Given, who was making a record 109th appearance for his country, to cancel out Shane Long's fifth-minute penalty.
However, Pedersen was not finished and as Ireland pressed for a late winner, it was he who provided the cross from which striker Erik Huseklepp fired the visitors to victory four minutes from time.
Up until that point, Giovanni Trapattoni's much-changed side had more than made a fist of a game against the kind of opponents they will have to find a way past if they are to make it to next summer's Euro 2012 finals.
But the veteran Italian's hopes of running the rule over some of the men he believes may have long-term futures in his squad while at the same time emerging with a positive result, were dashed at the end.
There were positives - Long proved an able deputy for injured skipper Robbie Keane, while Keith Fahey linked well with Glenn Whelan in central midfield.
But for a man who hates losing even friendly games, the late twist will have been hard to bear.
Trapattoni has made his name for being a coach who ultimately places results before entertainment, and he has made no bones about doing so during his reign in Ireland.
That approach very nearly took the Republic to the World Cup finals in South Africa and the 71-year-old hopes, despite last month's setback when Russia left the Aviva Stadium with all three points, that it will take them the extra step in their Euro 2012 qualifying campaign.
Given the opportunity to blood some of his emerging talents in tonight's friendly, he accepted it, but only to a point, deciding that a positive result against a side ranked 13th in FIFA's world rankings would be just as valuable.
With 15 minutes of the game gone, he could hardly have been better pleased with what he had seen.
Long's fifth minute run on to John O'Shea's through-ball caused the normally redoubtable Brede Hangeland all sorts of problems and prompted him to haul his man to the ground.
Icelandic referee Kristinn Jakobsson immediately pointed to the spot and with Keane absent, Long took over spot-kick duties and calmly despatched the ball low to goalkeeper Jon Knudsen's right and into the bottom corner.
A Norway side boasting nine of the men who started last month's qualifier victory in Cyprus, a win which maintained their 100% start, was at sixes and sevens in the opening stages, and they might have fallen further behind with 12 minutes gone.
Kevin Doyle's pass was perfectly weighted for Liam Lawrence to drive in a low cross, and although Knudsen palmed the ball just inches out of Long's reach it fell for Damien Duff. His left-foot drive was firm and accurate, but the keeper recovered to kick it off the line.
The Norwegians started to work their way into the game. John Arne Riise and Pedersen were finding space down the left as their side's passing became slicker and more penetrative, the pressure mounted.
Ireland's central midfielders, Fahey and Whelan, had enjoyed an encouraging start to the game, but they were bypassed 12 minutes before the break as Norway opened up their hosts.
Pedersen laid Hangeland's crisp pass off to Thorstein Helstad and Stephen Kelly handled as he slid in in an attempt to regain possession.
Pedersen took charge of the resulting free-kick and curled a superb left-foot shot high to Given's right to give Ireland's most-capped international no chance.
Stoke striker Jon Walters was handed a first cap as a half-time replacement for Doyle as Aiden McGeady came on for Lawrence, and their arrival prompted a flurry of activity.
Substitute keeper Espen Bugge Pettersen had to tip away a rising drive from long, but at the other end, Given proved equal to the task as Huseklepp went for goal twice within seconds.
But with Walters and Long repeatedly stretching the visitors' defence, Ireland were making much of the running.
The game opened up as time ran down with both sides looking for a winner, and it took a brave block by Whelan to keep out Riise's 76th-minute piledriver from getting anywhere near Given.
However, the Manchester City man was beaten for the second time with four minutes remaining when Pedersen's cross left him cruelly exposed and Huseklepp took full advantage at the far post to snatch victory.