Two goals in the final 15 minutes finally ended the fight of the plucky visitors, who had turned the game into a nervy affair with a second-half equaliser.
But a header from Clint Dempsey, which ricocheted in off the goalkeeper, and a typically cool finish from Jermain Defoe ensured Spurs finished second to Lazio in Group J and will join Liverpool, Chelsea and Newcastle in the draw on 20th December.
The game seemed set to be a procession as Tottenham started on the front foot against a side who seemed reluctant to venture outside their own half.
But, despite dominating possession, the home side seemed to miss the penetration of the missing Gareth Bale and it took them until the 29th minute to make their dominance pay.
Finally a precise through ball from Clint Dempsey fell perfectly into the path of Emmanuel Adebayor, who slotted coolly past goalkeeper Orestis Karnezis.
There was little threat from Panathinaikos, despite them knowing they needed victory to preserve their place in the competition, and White Hart Lane sat back and waited for more.
Maybe it was too easy for Andre Villas Boas' side, who failed to make their dominance show on the scoreboard, and they were punished after 54 minutes when, out of the blue, Zeca got on the end of a cross from the impressive Spyropoulos to direct a great header past Brad Friedel.
Suddenly there was a nervous edge to the atmosphere as the crowd and players faced the fact that one more slip could see them eliminated.
And the few thousand Greek fans were certainly making themselves heard in the freezing air at White Hart Lane as their side pushed forward with a renewed belief - top scorer Toche having their best chance when he poked agonisingly wide following a mix-up in the Spurs back-line.
But after 20 minutes of nail-biting from the capacity crowd in North London, Tottenham finally made sure of their place in the draw for the next round.
A free-kick swung in by Kyle Walker was headed against the underside of the crossbar by Clint Dempsey, but the ball hit the unfortunate goalkeeper on its way out and nestled in the back of the net.
And the scoreline was given some sense of realism five minutes later as Defoe latched on to a ball from Aaron Lennon to clip it over the advancing goalkeeper.