Luisao's header from a Pablo Aimar corner made it 4-0, and Di Maria set up Saviola for the final goal.
He can call on Iceland striker Eidur Gudjohnsen and Argentina's Javier Saviola while Lionel Messi, Ludovic Giuly and Ronaldinho provide further options.
Both sides made half-time changes, with Massimo Maccarone coming on for James Morrison and former Spurs striker Kanoute coming on for Javier Saviola.
Benfica's two wide men, Di Maria and the Brazilian youngster Ramires, carved out an early opportunity for Saviola, but he had strayed narrowly off-side.
Easily losing his marker, the debutant Seamus Coleman, Saviola drove his right-footed volley across goal, and a diving Tim Howard was unable to reach the shot.
The second half was a different story, with the skills and pace of halftime substitutes Saviola and Riquelme, and later Overmars, helping Barca step up a gear.
But Argentine forward Javier Saviola exchanged passes with fellow substitute Juan Roman Riquelme to put the visitors back into the game three minutes into the second half.
Instead, the final goal was scored by Saviola after David Luiz's long ball had found Di Maria racing past Hibbert for the umpteenth time of the night.
Angel di Maria played a blinder on the left wing, setting up the first three goals - the opener for Javier Saviola, and the next two for Oscar Cardozo.
Leverkusen's Argentine defender Diego Placente bore most responsibility for his side's defeat, losing the ball on the half-way line for the move that led to Saviola's goal and committing other defensive blunders.
Then came Benfica's opener: Di Maria, who frequently caused Tony Hibbert and Dan Gosling a host of problems with his pace and trickery down the left flank, delivered an inch-perfect cross for his fellow Argentinian Saviola.
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