Striker Rodrigo Lima handed Benfica a 1-0 first-leg advantage as they took a step towards the last 16 of the Europa League in Greece.
Lima's 59th-minute strike was enough to clinch a 1-0 victory over PAOK Salonika and leave the Portuguese side in pole position ahead of next week's return in Lisbon.
Benfica, who dropped into the competition after finishing third behind Paris St Germain and Olympiacos in Champions League Group C, shaded a game of few clear-cut chances.
In a tight first-half, neither side was able to create much of any note with neither PAOK goalkeeper Panagiotis Glykos nor opposite number Artur called upon to deal with anything other than an occasional set-piece.
Midfielder Sekou Oliseh passed up the home side's only real opportunity when he fired wide with eight minutes gone, while defender Silvio was no more successful for Benfica on the half-hour.
However, a keenly-contested 45 minutes saw PAOK's Ergis Kace and Costin Lazar and the Portuguese side's Andre Gomes all go into German referee Wolfgang Stark's notebook for fouls.
Lazar went close for the Greeks three minutes after the restart, and his miss was to prove costly as Benfica forced their way in front with 59 minutes gone when Lima fired right-footed past Glykos from Filip Djuricic's pass.
Substitute Lazar Markovic forced an 82nd-minute save from Glykos as the visitors went for the kill, but Artur denied Konstantinos Katsouranis an equaliser with four minutes remaining with PAOK fighting for a way back into the game.