The Czechs who had not qualified for the World Cup since becoming an independent nation after their last appearance as Czechoslovakia in Italy in 1990 needed only a draw after winning the first leg in Oslo 1-0.
Rosicky gave the Czechs insurance in the 35th minute however driving a low shot into the corner of the net after Milan Baros's effort just inside the penalty area deflected off John Arne Riise.
'This is the peak of my career' Czech coach Karel Brueckner said moments before his players picked him up and carried him on the field to the delight of the crowd. 'We showed our character tonight I'm proud of how they played.'
Even without injured strikers Jan Koller and Vratislav Lokvenc the Czechs made a fast start and Vladimir Smicer and Baros went close.
Playing with the skipper's arm band on for the first time in over 16 months midfielder Pavel Nedved controlled the tempo of the match as the Czechs showed their class in building attacks.
Smicer again went close in the 31st minute when he glanced the ball off the post after a Marek Jankulovski corner.
Minutes later Baros turned and tried to fire a shot on goal but Riise got a leg to the ball. It bounced across the penalty area to the unmarked Rosicky who drove a low volley past goalkeeper Thomas Myhre.
The Norwegians regrouped narrowly missing several chances before the interval and pressing for much of the second half.
The Euro 2004 semi-finalists never cracked however and goalkeeper Petr Cech made several fine saves to record his second successive clean sheet.
'In the second half we were better we had possibilities but we are a young team and we need some experience now' Norway striker John Carew said.
'We have a lot of talent and I hope in the next qualifying campaign we will have the experience we need.'
Tempers flared near fulltime when Riise fouled Zdenek Grygera as the two tried to head the ball. Riise appeared to come off worse lying prone on the ground for several minutes and receiving a yellow card.