Everything looked rosy at the break with us 1-0 up through Emmanuel Adebayor, but the Greeks, needing to win to progress, looked a different team in the second half, levelled and put us under pressure for a 15-minute spell.
That spell was snapped by Dempsey's powerful header from the impressive Kyle Walker's free-kick on 76 minutes and then Defoe underlined his confidence with a delightful finish from Aaron Lennon's pass in the 83rd minute. Lennon was another stand-out performer.
Andre Villas-Boas made four changes from the win at Fulham. Two were forced with Gareth Bale and Michael Dawson picking up injuries at Craven Cottage, and they were replaced by Kyle Walker and Emmanuel Adebayor. Tom Carroll also returned for Mousa Dembele and Brad Freidel was back in goal and captained the team.
The first half was a cagey affair as Panathinaikos appeared happy to concede possession and hit us on the break.
Chances were few and far between but things started to warm-up midway through the half when the visitors had their only sight of goal, Toche helping Giourkas Seitaridis' free-kick into Friedel's hands.
Dempsey soon fired wide and we took the lead on 28 minutes. Walker picked the ball up in central midfield and found Dempsey, he picked out Adebayor and the big man made no mistake, stroking home past Orestis Karnezis.
Sandro rifled over after good work from Adebayor and Aaron Lennon and Jermain Defoe lashed over the final chance of the half after Dempsey went up for Lennon's cross.
As expected, needing to win, Panathinaikos pushed on to 4-3-3 when they attacked in the second half.
It could have been 2-0 inside five minutes as Dempsey found another defence-splitting pass into Defoe, who controlled and drilled low onto the inside of the post.
Panathinaikos enjoyed more possession and were back in the game in the 54th minute. Giourkas Spyropoulos crossed deep from the left and Zeca planted his header into the far corner.
Spyropoulos' crosses from the left became a theme over the next 15 minutes and two created chances. The first fell to Toche, who should really have done better from eight yards and then Jan Vertonghen was forced into a vital glance away as Toche looked to attack at the far post in the 74th minute.
Any nagging doubts were put to bed two minutes later. The goal owed much to Sandro's lung-bursting run down the right, which eventually ended with the award of a free-kick. Walker curled in and Dempsey powered a free header home off the underside of the crossbar, with a little help from Karnezis' back.
The clincher was a beauty. This was all about Lennon, who cut across from right to left and then played a reverse pass into Defoe, who dinked over Karnezis and home.
Spurs (4-4-2): Friedel; Walker, Caulker, Vertonghen, Naughton; Lennon (Livermore, 87), Carroll (Dembele, 74), Sandro, Dempsey (Sigurdsson, 80); Adebayor, Defoe. Unused subs: Cudicini, Stewart, Huddlestone, Townsend.
Panathinaikos (4-4-1-1): Karnezis; Seitaridis, Triantafyllopouous, Vyntra, Spyropoulos; Zeca, Vitolo, Sow (Christodoulopoulos, 60), Mavrias (Fornali, 84); Sissoko; Toche (Petropoulos, 78). Unused subs: Kapino, Marinos, Chouchoumis, Velaquez.
Yellow cards: Spurs - Naughton. Panathinaikos - Spyropoulos.
Goals: Spurs - Adebayor (28), Dempsey (76), Defoe (83). Panathinaikos - Zeca (54).
Referee: Mr P Gil (Poland).