The Premier League's top three clubs go into the first round of the Champions League proper, with the fourth-placed side set for a qualifying round.
However, Chelsea could scupper the qualification hopes of any other side that finish fourth by winning this season's Champions League.
Chelsea are the only English side left in the tournament, although they are up against defending champions Barcelona in the semi-finals.
At St James' Park, France midfielder Hatem Ben Arfa gave Newcastle a sensational 73rd minute lead when he beat several defenders before slipping the ball into the corner.
Newcastle and Senegal striker Papiss Demba Cisse then made it 10 goals in nine games when, from close range, he turned in Shola Ameobi's cross seven minutes from time.
"It was a special, special goal from Ben Arfa," Newcastle manager Alan Pardew told Sky Sports.
"He's got that magic touch. Hopefully, it will edge the French manager (Laurent Blanc) to include him in the French squad (for Euro 2012)."
Tottenham fell behind at White Hart Lane when Anthony Pilkington fired the Canaries into a 13th minute lead.
But England striker Jermain Defoe drew Tottenham level 20 minutes later.
However, Norwich saw winger Elliott Bennett lash the ball past Brad Friedel as the Spurs defence backed off to make it 2-1 in the 66th minute.
Defeat meant Tottenham had won just once in eight league games.
"Credit to them (Norwich) as I think they deserved it," said Tottenham manager Harry Redknapp. "It was a bad day but we have to pick ourselves up."
Everton warmed up for their FA Cup semi-final against Merseyside rivals Liverpool at Wembley on Saturday by thrashing Sunderland 4-0 at Goodison Park.
All of the home side's goals came in a second-half spree, with winger Magaye Gueye firing Everton ahead in the 52nd minute.
The Frenchman then turned provider as South Africa's Steven Pienaar sealed victory with a 75th minute shot from the edge of the box.
Barely 60 seconds later Leon Osman made it 3-0 before Nigerian striker Victor Anichebe added a fourth nine minutes from time, with Everton resting several players ahead of the Cup semi-final.
Victory also saw seventh-placed Everton go four points clear of Liverpool in their bid to finish above their neighbours for the first time since 2005.
Elsewhere, Aston Villa opened up a seven-point gap between themselves and the bottom three with six games to play after a 1-1 draw at home to Stoke.
Andreas Weimann's 32nd minute curling shot put Villa ahead before Robert Huth equalised for Stoke when he headed in a free-kick 19 minutes from time.
-AAP