Alexis Sanchez struck after six minutes and Cesc Fabregas added a second following the break to leave Barca with a 100 per cent record from their opening two games while Celtic are on four points following their earlier win away to Spartak Moscow.
Sergio Busquets was sent off with two minutes to go after a clash with Maxi Pereira.
Tito Vilanova arrived at the Camp Nou over the summer looking to win back the Champions League, which they have lifted twice out of the last four years, and the domestic league title.
And despite the pressure of replacing Pep Guardiola he could hardly have made a better start with also six wins from six in la liga.
Now Vilanova's men turn their attention to the small matter of the El Clasico on Sunday against Real Madrid - but they will be without Carles Puyol, who dislocated an elbow after falling heavily on his arm.
"It was a costly victory for us but we are happy with the result against Benfica who are a strong side. It was a nasty injury (for Puyol) and he has already had one this season so this isn't very normal," said Vilanova.
"We have had a lot of problems at the back and it would be nice to play the El Clasico with a full squad but still we are playing well at the moment and have five days to recover."
Benfica coach Jorge Jesus had only words of praise for his players.
"We weren't lacking in any area. We were against the side who in my opinion is the best in the world and in any game they have about 70 percent possession. We were excellent in the first half and didn't deserve to go in losing," he said.
"At 2-0 Barca consolidated, defended the result and made it difficult to come back at them."
The main news for Barcelona before kick off had been that Puyol was returning from injury to lead the team from the back while Andres Iniesta was fit for a place on the bench.
For Benfica seeking their first victory against a Spanish side since the 1982-83 season they were missing defender Luisao and up front Oscar Cardoza, while playmaker Pablo Aimar, who had overcome a strain, was left out of the starting eleven as Jorge Jesus sought a more mobile midfield.
The home side began at a blistering pace with a well-worked move seeing Bruno Cesar cracking a left-foot shot from the edge of the area that was too central and keeper Victor Valdes parried.
But Benfica found themselves behind after Barcelona's first attack of the match as with Pereira pressing forward from right-back, Leo Messi found space on the left of the area and crossed for Sanchez to slide the ball home and end a barren spell which had seen him not hit the back of the net since last April.
Benfica quickly returned to the offensive and Puyol and Javier Mascherano were being run ragged while they received little protection from their midfield. Rodrigo Lima burst through and Valdes saved well with his feet and then after 16 minutes Osvaldo Gaitan volleyed over from 15 yards.
As the first half progressed Barca began to find their composure and assert themselves on the midfield although the Portuguese continued to bite at their heels.
In a reverse of the first goal Sanchez on the left of the area found Messi, who forced a fine save from keeper Artur Moraes before Sanchez fired over.
Benfica were using the strategy of harrying Barca's midfielders which was used with some success by Chelsea and Real Madrid last season.
But almost every time the visitors did break they went close to scoring. A Sanchez effort was blocked by Artur and then on the point of half-time a Pedro Rodriguez cross was just too long for Messi.
Benfica brought the more attack-minded Carlos Martins into midfield but Barca started to dominate in the second half and got their second goal through an in-form Cesc. He latched onto a Messi pass and finished clinically on his left foot past Artur.
Benfica went close with headers from Jardel Vieira and Nemanja Matic but Barca were in control and the only stains on their evening were the injury for Puyol and Busquets' harsh expulsion late on when he seemed to make little contact with Pereira when they jumped for a ball.