Helder Postiga scored the 53rd-minute winner for Portugal in the top-of-the-table match in Lisbon, securing his side a third successive victory in qualifying since Paulo Bento took over as coach in September.
England came from 2-0 down to grab a point at Wembley and only remained top of its group on goal difference from Montenegro, which missed a chance to go above Fabio Capello's side by drawing 1-1 to Bulgaria.
Greece eased past Malta 3-1 to return to the top of Group F and Robbie Keane's double earned Ireland a 2-0 victory at Macedonia, keeping Giovanni Trapattoni's side first in Group B ahead on goals scored from Russia and Slovakia - who both won on Saturday.
Postiga pounced at the near post to poke home a cross from winger Nani as Portugal, captained by a subdued Cristiano Ronaldo, finally broke down an obdurate Norway defense.
“This game was no less harder than we'd expected,” said Bento, who has revived Portugal's campaign since taking over from Carlos Queiroz when the team was on just one point from two qualifying games. “We managed to take control and keep control.” Denmark tied with Portugal and Norway in the standings with a 2-0 win at Iceland, with midfielders Lasse Schone and Christian Eriksen scoring second-half goals in Reykjavik.
Like Portugal, England's place at Euro 2012 is far from secure after being held by Switzerland.
Tranquillo Barnetta scored two free kicks in the space of three minutes to put the Swiss 2-0 ahead by the 35th but Frank Lampard pulled one back from the penalty spot for England in the 37th minute.
Substitute Ashley Young leveled with a powerful strike six minutes into the second half.
“The Switzerland players were fresher, they have had a different season,” said England coach Fabio Capello. “We suffered because we arrived without energy.” Switzerland is six points behind the joint leaders with three matches left. Only the top team qualifies automatically from each group.
“To draw in the home of football is very good, but we don't want to overestimate it. We have to go on,” Switzerland coach Ottmar Hitzfeld said.
Montenegro failed to take advantage of England's slip-up, conceding a goal to Ivelin Popov in the 64th to draw with Bulgaria.
Radomir Djalovic put the hosts ahead in the 52nd with a volley from Vladimir Bozovic's left wing cross.
“We are fine with this draw, but it is a pity that we did not score a positive result,” Montenegro coach Zlatko Kranjcar said.
All three of Group B's pacesetters won to leave the pool wide open with four matches left for each side.
Keane became the first British player to reach the 50-goal mark in internationals, moving onto 51 with his brace in Macedonia.
Roman Pavlyuchenko, Keane's teammate at English side Tottenham, scored a hat trick in Russia's 3-1 home win over Armenia and Slovakia edged past Andorra 1-0 thanks to Miroslav Karhan's 63rd-minute winner.
In Group F, Yiannis Fetfatzidis scored twice and Kyriakos Papadopoulos added a goal on debut to help visiting Greece beat Malta.
Michael Mifsud scored Malta's lone goal.
Israel stayed one point behind Greece and level on points with Croatia after a 2-1 victory at Latvia.
