Sloppy marking from Sebastien Bassong allowed Dimitris Salpingidis and Stefanos Athanasiadis to give the Greeks a 2-0 lead after 13 minutes at White Hart Lane but Spurs pulled one back with a Luka Modric penalty after Konstantinos Stafylidis was dismissed for handball on the line.
Tottenham thought they had equalised through Jermain Defoe in the second half, but referee Bas Nijhuis controversially disallowed the striker's goal for a foul on Pablo Contreras.
The result put PAOK through and left Spurs needing to hammer Shamrock Rovers in Ireland in a fortnight's time and hope the Greeks overcome Rubin Kazan in Thessaloniki.
Harry Redknapp, taking charge of his first European game since undergoing heart surgery three weeks ago, named a strong Spurs side including Jermain Defoe, Aaron Lennon and Modric.
The Spurs boss may have been hoping for a relaxing opening 15 minutes, but it did not materialise as wretched defending allowed the Greeks to open up a two-goal lead.
Willed on by the raucous hordes who had made the trip from Greece, PAOK took the lead in the sixth minute.
William Gallas lost the ball coming out of defence and Giorgos Georgiadis took advantage, running into space down the right flank before crossing to the unmarked Salpingidis, who carefully guided the ball past an off-balance Heurelho Gomes after losing Bassong.
Seven minutes later PAOK were 2-0 up. Pablo Garcia released Georgiadis down the left wing and he swung a low ball across the box which Athanasiadis tapped home after being left in yards of space by sloppy marking, again from Bassong.
The rowdy away fans, many of whom were topless despite it being a chilly night, urged their team to score a third and they almost obliged when Giorgos Fotakis found space in the box but his shot was deflected wide by Vedran Corluka.
Defoe wasted Spurs' only chance of the opening 25 minutes when he blasted wide from just outside the box.
Danny Rose put in a desperate block to deny Athanasiadis' fierce drive as the Greeks continued to dominate.
With 36 minutes gone, Defoe finally tested Kostas Chalkias, firing a brilliant shot which the Greek stopper tipped wide.
Corluka saw his header cleared off the line from the resulting corner by Stafylidis and the ball rebounded to Harry Kane. The youngster aimed at goal again, and Stafylidis blocked again, but referee Bas Nijhuis ruled the PAOK full-back had used his hand on the second clearance and he was given a straight red.
Modric stepped up to take the resulting penalty and he made no mistake to pull one back for Spurs to make it 2-1 with nine minutes of the first half left.
Spurs thought they had equalised just after the break when Gallas tapped home Modric's cross, but the PAOK defensive line had moved up just in time to rule the Frenchman's effort out for offside.
Rose's skills gave him time to cross to the back post, but Kane headed over from eight yards.
Kane played a delightful one-two with Corluka to send the Croatian free down the right but his cross was met by a poor miscue from Steven Pienaar.
Tottenham's numerical advantage started to show as they dominated possession, but the equaliser was still missing.
Bassong, Lennon and Jake Livermore all had shots blocked as Spurs threw everything at PAOK, who were defending with all 10 of their players behind the ball.
Redknapp injected more pace into his side by introducing Gareth Bale and Kyle Walker.
Walker pinged a cross just over Kane's head and the ball fell to Bale but his shot sailed over the bar.
Redknapp barked orders from the touchline and the home fans became restless as Tottenham failed to test Chalkias despite their numerical superiority.
The home side had the ball in the net with 15 minutes left but the goal was controversially ruled out.
Yago Falque's shot was cleared off the line by a diving tackle from Contreras and the midfielder sprung to his feet to stop a sliding Defoe from tapping in from two yards with a brave challenge which saw the England striker's studs sink in to the PAOK player.
Contreras lay stricken on the floor clutching his leg, but the game continued. Spurs swung the ball back in to the box and Defoe toe-poked in past Chalkias to score what he thought was the equaliser.
The referee appeared to give a goal but after deliberating with his assistant behind the net, gave a free-kick to the Greeks.
Spurs' players were furious at the decision but, willed on by an angry home crowd, kept pushing for a second.
Falque curled wide and Gallas had an effort cleared off the line before Spurs were given a free-kick 25 yards out in injury time.
Bale stepped up to take it but Chalkias gathered comfortably and PAOK hung on for the win.