Despite the Londoners enjoying the majority of possession, they struggled to show much attacking spark during the opening 45 minutes.
Meanwhile, their Greek hosts rarely threatened Hugo Lloris in the Tottenham goal.
The away side made the breakthrough 10 minutes before the half-time whistle as Dawson nodded in from Tom Huddlestone's free kick.
Huddlestone nearly doubled their lead towards the end of the half, but his drive was pushed away by Panathinaikos goalkeeper Orestis Karnezis.
Jermain Defoe, who looked frustrated in attack for much of the night, should have made it 2-0 early in the second half - only to blaze his shot over the crossbar after some good control.
Their wastefulness in front of goal was punished with 13 minutes left on the clock when Toche poked the ball past Lloris from Giourkas Seitaridis's clever through ball.