The Manchester United forward finished off a sweeping counter attack on nine minutes as he left Fulham defender Brede Hangeland for dead before drilling a low shot beyond home goalkeeper Rune Almenning Jarstein from inside the home area.
England could and should have been ahead in the fourth minute when Stewart Downing picked out Liverpool team-mate Andy Carroll only to see the rampaging forward head wide from six yards out when he seemed likelier to hit the rigging.
England had not beaten Norway in some 32 years. The result was better than the performance with neither side producing too much quality in the final third. It was their first win in Oslo since 1966.
The last time England managed to overcome Norway was when Terry McDermott scored twice in a 4-0 win in a World Cup qualifier at Wembley in 1980, but they were clearly a class above an average home side, who were routed 4-1 in Wales last year and who continue to fraternise with a predictable physical style under coach Egil Olsen.
Norway had plenty of possession in the second half, but England were rarely troubled despite being forced to defend in numbers. A better side would have equalised with the amount of ball the home side enjoyed, but were fairly predictable with a number of high balls causing Phil Jagielka and Joleon Lescott few problems at the heart of the visiting defence.
Norway did little of real note in the first period, but Morten Gamst Pedersen almost embarrassed visiting goalkeeper Rob Green on 13 minutes when his delivery came back off a post with the West Ham man beaten at his near post.
He headed into the home area, but could only slam a shot straight at Jarstein who made a comfortable enough save.
Green did fist away a blistering shot from John Arne Riise in the second half while Mohammed Abdellaoue had a valid claim for a penalty when he tumbled under pressure from Leighton Baines, but England never looked like conceding despite giving the ball away far too cheaply the longer the evening progressed.
Steven Gerrard was replaced at half-time by Gareth Barry after Gerrard was fortunate to avoid a red card for a two-footed tackle on Tom Hogli in the first half. Gerrard won the ball from Hogli who was forced out of the action with the Liverpool captain careering into the challenge with both feet off the ground.
Jordan Henderson replaced Barry in the second half, who will have a groin strain assessed over the next few days. Hodgson also handed a debut to Arsenal teenager Alex Oxlade-Chamberlain, but there are likely to be several changes to Hodgson's team in their next outing.
England play their final match before the Euro 2012 finals when they face Belgium at Wembley next Saturday. They play their first match at the finals against France in Donetsk on June 11 in a Group D section that also contains Ukraine and Sweden.