Elsewhere, Frank Lampard became the first midfield player to chalk up 150 Premier League goals as Chelsea were held to a 1-1 draw at West London neighbours Fulham.
Fourth-placed Spurs and Newcastle, in fifth, are now level on 59 points in the race for the fourth and final Champions League qualifying berth for next season with Chelsea two points adrift in sixth position.
"I thought Norwich bullied us a little bit. It was a difficult day for our boys at the back," Spurs manager Harry Redknapp told reporters.
"Credit to them, I think they deserved it. We were disappointing," he added, as Spurs continued a poor run that has yielded one win in eight league games.
"He's got that bit of magic," said Newcastle manager Alan Pardew. "Hopefully it will persuade his manager to include him in the French squad."
Chelsea's interim coach Roberto Di Matteo, who has been on the losing side just once in his 11 matches in charge, praised Lampard for reaching his goal landmark.
"It shows what a tremendous player he's been for Chelsea over the years," said Di Matteo who again rang the changes in his starting line-up as the squad continued their hectic schedule in the Premier League, Champions League and FA Cup.
"I thought we were mainly in control of this game but maybe we didn't pose enough threat for a second goal. We're hanging in there and getting closer to the teams ahead of us though."
