Cesar netted with assurity in the 40th minute after midfielder Nicolas Gaitan had created the opening for him, giving the Portuguese side a deserved victory.
Benfica imposed themselves on the game from the kick-off, Oscar Cardozo earning a first-minute free-kick in Galati territory. Cesar took it and found Luisao at the back post, but he could not put the ball back across to a team-mate despite being unmarked.
Gaitan lashed a shot wide of the post from the visitors' next chance in the eighth minute, Cardozo again involved as he lofted the ball into the penalty area.
Axel Witsel's shot failed to find its way through a sea of bodies moments later as the home side continued to soak up pressure.
For the next 20 minutes Benfica dominated possession but failed to create a clear chance, Cesar breaking that trend when fizzing a shot wide after half an hour.
Javier Saviola's run and shot kept Branko Grahovac alert in the Galati goal but he could not stop Cesar putting his side ahead five minutes from the interval.
Gaitan was the creator, playing a delicate ball over the defence and finding Cesar, who showed plenty of composure in slotting home.
Having failed to muster anything positive in the opening 45 minutes, the Romanian side's manager Dorinel Munteanu made one change at the interval - with Gabriel Viglianti coming on for John Ibeh in midfield.
Galati's first shot of the match followed soon after the restart, midfielder Gabriel Giurgiu curling left-footed from 25 yards but missing the far post.
As in the middle stages of the first half, Benfica moved the ball to the flanks where possible but the Romanian side looked relatively comfortable clearing crosses and kept their opponents at bay.
Emerson tried something a little more direct when he shot from the left channel in the 55th minute but Grahovac was left with an easy save.
There was a chance of an unlikely equaliser on the hour when Benfica goalkeeper Artur made a double intervention, first punching clear Ioan Filip's shot, then tipping Liviu Antal's follow-up effort round the post.
Benfica returned fire through Cardozo and Cesar, but Grahovac continued to stand firm.
Cesar and Cardozo both tried their luck in the 66th minute - but Grahovac parried Cesar's 25-yard effort and caught Cardozo's 20-yard shot.
The hosts tried their luck twice in the closing stages, but substitute Sorin Frunza's 18-yard effort in the 90th minute was parried by Artur, while Milan Perendija's effort from a similar range soon after failed to test the Benfica goalkeeper.