The Rennes midfielder's 77th-minute header cancelled out Oleg Shatov's early opener as Fabio Capello's FIFA World Cup-bound Russia were left with much to ponder.
Despite making it nine matches unbeaten since the shock 1-0 reverse to Northern Ireland in a FIFA World Cup qualifier in August last year, Russia were less than impressive in Oslo.
Having recorded an unconvincing 1-0 over Slovakia on Monday, the visitors raced into a third-minute lead as Shatov capitalised on some hesitant defending to finish from close range at the second attempt.
Norway, who have won just once in the last 10 games, lost 4-0 against France on Tuesday and looked vulnerable against Capello's side whenever the ball came into the box.
But they improved after the interval and were rewarded when Konradsen headed in Morten Gamst Pedersen's cross via the far post.
It will cause some concern for Russia - who qualified for the World Cup ahead of Portugal in UEFA Group F - going into their tournament opener against South Korea on June 17, with matches against Belgium and Algeria to follow.
The visitors, who were without midfielder and captain Roman Shirokov once again through injury, signalled their intent from the start.
Shatov saw his initial shot from inside the box blocked before retrieving the loose ball to steer it past goalkeeper Rune Almenning Jarstein.
A long-range Havard Nordtveit free-kick called Russia keeper Igor Akinfeev into action midway through the half, but the hosts were immediately under pressure at the other end as Jarstein produced a finger-tip save to keep out Denis Glushakov's header.
Capello made three changes at half-time, with Aleksandr Kerzhakov - scorer of the winning goal against Slovakia - among those to make way.
Norway coach Per-Mathias Hogmo looked increasingly restless on the touchline but was afforded some relief when Pedersen's excellent delivery picked out Konradsen to level the scores.
The hosts were the better side for the remaining 13 minutes, but Russia, who have a home friendly against Morocco on Friday before heading to Brazil, held on.
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