Abdoulaye Faye headed against the post early on for the Magpies, who took the lead when Michael Dawson's mistake let Obafemi Martins in to fire home.
Dawson also gave Claudio Cacapa room to head home a second after half-time.
Robbie Keane replied for Spurs from close range after Darren Bent's header hit the post but James Milner's sweet volley sealed victory for Newcastle.