The only goal of the game came seconds before the interval as man of the match Aiden McGeady's shot took a deflection off Luisao and found the back of the net.
Benfica dominated the early stages of the game and even when Celtic did gain possession, the visitors always looked dangerous on the break.
Artur Boruc passed his early tests with flying colours, saving well from Oscar Cardozo on two occasions in the opening minutes.
At the other end McGeady showed early promise, winning a dangerous free-kick, but John Kennedy misplaced his header and passed up a great chance.
Scott Brown took his chance with a long-range effort which was scrambled away by Benfica goalkeeper Quim.
Scott McDonald also had a go from the edge of the box, but his effort was easily gathered and Celtic were nearly made to pay as Benfica raced away on the counter-attack.
The Celtic defence looked nervous and the visitors looked the more likely to score with Rui Costa dictating the play.
But despite their early scares, Celtic made the breakthrough with half-time rapidly approaching as McGeady struck from 20 yards out to send his side off in the lead.
The Hoops upped the tempo of the game in the second half and Benfica quickly began to look tired and ragged, particularly at the back. Rui Costa's cutting edge from the first half had deserted him and McGeady became the main dangerman on the pitch.
He tormented the Benfica defence with his pace down the left wing and kept his side in control of the game.
Only Cardozo continued to pose any real threat for the visitors but his best effort, a header from close range, went wide of the target.
Brown had a golden opportunity to put the game further out of the reach of the Portuguese midway through the half as he raced on to a McDonald pass to blast his shot at Quim, who could only punch it way. Brown picked up the rebound but hit his second effort wide.
An otherwise excellent match ended in acrimony as Augustin Binya was sent off for a crude tackle on Brown that ended the Celtic midfielder's evening and brought a well-merited straight red card.