Playing in the competition for the first time in four seasons, the Scottish giants were unable to mark their return in style against opposition they had beaten in Glasgow three times previously.
Neither side were able to create anything resembling a clear opportunity in the first half, with Benfica goalkeeper Artur not having to make a save in the opening 45 minutes.
There were a few more opportunities after the break, but both defences held firm to earn a share of the points.
"I'm pleased," Celtic manager Neil Lennon told Sky Sports.
"It was a tough game against a quality side, I though we played very, very well.
"I thought that we lacked a little bit of a cutting edge in the final third but it's a decent start for us, five clean sheets in a row in Europe, so we can take a lot from that, but I think we'll improve as the tournament goes on."
BRIGHT START
To the delight of the Celtic faithful their side, missing key striker Georgios Samaras due to an elbow injury, started brightly, despite having only their impressive captain Scott Brown with previous Champions League experience.
That did not translate into a serious attacking threat, however, and despite new signing Miku and Kris Commons looking lively, the Benfica defence was largely untroubled, one clearance from Jardel aside.
Benfica, themselves missing suspended captain Luisao and Maxi Pereira and with leading striker Oscar Cardozo on the bench, were just as impotent at the other end.
Their only chance fell to Rodrigo on 31 minutes, who got behind the Celtic defence but not keeper Fraser Forster, despite suggestions he may have impeded the attacker.
The second half followed a similar script, with plenty of hustle in midfield and end-to-end play, but little end product.
Forster had to be alert to keep out Ezequiel Garay from a corner, while Commons had a shot from well outside the box with Artur off his line, but neither keeper was seriously under threat as their sides settled for a deserved share of the spoils.
Lennon's side will next travel to Spartak Moscow, who conceded two goals in the final 20 minutes to lose their opener against Barcelona 3-2.
