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 properly test Artur in the Benfica goal.
The hosts dominated the opening half an hour of the game, but it was Benfica which 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 off the ball, Rodrigo was flagged for a marginal offside.
Celtic was 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 its 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.
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.
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 center 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.