A second-half strike by Raphinha gave Barcelona a 1-0 advantage to take back home for next week’s second leg against Benfica.
The Portuguese side came into the match as underdogs but showed their early threat through striker Vangelis Pavlidis.
The task for Hansi Flick’s side became harder in the 22nd minute when defender Pau Cubarsi was shown a straight red card for fouling Pavlidis, who was otherwise through on goal.
Despite being down to 10 men, Barcelona managed the game and on the rare occasions Pavlidis and Orkun Kokcu got through, goalkeeper Wojciech Szczesny denied them.
Then in the 61st minute, Raphinha capitalised on a defensive error and ruthlessly fired home the winner.
Benfica threw everything forward late on but substitute Renato Sanches saw his volley matched by Szczesny as the visitors held on.