The visitors took the lead with a well-worked goal after just six minutes.
Lionel Messi and Xavi were both involved in the build-up play, before Alexis Sanchez applied the finish from inside the box.
Benfica could have been level just five minutes later, when Lima scampered through on goal. However, the Brazilian saw his effort well saved by Victor Valdes.
The Catalan outfit doubled their advantage 10 minutes after half-time. Messi was the architect, as he went on a winding run before laying the ball off to the ensuing Cesc Fabregas, who blasted past Artur.