The visitors went closest through Rodrigo but both sides struggled to dominate in an evenly-matched Group G clash at Celtic Park
Rodrigo had the best chance of the game for the visitors after a clever pass from Pablo Aimar, but was thwarted by Fraser Forster.
Neil Lennon’s side probed throughout via the industrious Kris Commons, but failed to test properly test Artur in the Benfica goal.
Celtic were without Gary Hooper in their starting XI after the striker failed a late fitness test and had to make do with a place on the bench, but the hosts started brightly as Commons tried his luck with a chip from long range before fluffing a shot after a clever pass from Miku.
The hosts dominated the opening half an hour of the game, but it was Benfica who went closest with the first genuine chance.
The Benfica midfield had been stifled by the energetic Victor Wanyama – who picked up a yellow card for a pull on Enzo Perez - but Aimar found enough space to lift a ball over the Celtic back four and into the path of Rodrigo, whose stabbed effort was foiled by the onrushing Forster.
Jorge Jesus’s side improved as the half went on and saw an Ezequiel Garay shot from the edge of the area fly high over the crossbar as both teams struggled to create openings.
And towards the end of the first half, when the visitors thought they had a clear chance at goal after hustling Emilio Izaguirre – who was earlier yellow carded for a late challenge on Eduardo Salvio – off the ball, Rodrigo was flagged for a marginal offside.
Celtic were again in the ascendancy at the start of the second half without calling Benfica goalkeeper Artur into action, as Adam Matthews went closest with a shot from the edge of the area which was deflected over for a corner.
But with an hour gone, the Portuguese side showed a glimpse of their quality as Rodrigo shimmied into the box to play in Aimar who set the ball into the path of Nicolas Gaitan, but the forward’s effort was cleared.
Garay forced Forster into a save low at his near post from the resulting set piece and Celtic eventually cleared, before Oscar Cardozo replaced Aimar for the visitors, while Thomas Rogne came on for Mikael Lustig.
The hosts had their best chance of the half shortly after when Commons’ clever turn and cross caught Nemanja Matic off guard, but the Chelsea man’s deflection was kept out of his own net by the alert Artur.
Hooper was introduced in place of Izaguirre with just over 20 minutes to play, but Celtic again failed to make a succession of corners count.
Both sides tried their luck from ambitious distance heading into the closing stages, as second half substitute Bruno Cesar blasted over from 30 yards for Benfica, before Commons nearly caught Artur off his line from the centre circle but the keeper hurried back to save comfortably.
Cardozo saw a late header flash over the bar and Celtic pressed in stoppage time, but both sides begin Group G with a point.