It was a spirited and determined performance from the Scottish champions but over the course of 90 hard-fought minutes they failed to really trouble the visitors' goal.
Indeed, in terms of chances created, the Portuguese side could perhaps claim to have edged it, with Hoops keeper Fraser Forster forced into a good blocking save from Rodrigo in the first half and another at his near post from Ezequiel Garay after the break.
Next up for Celtic in Europe is an away trip to Spartak Moscow next month where boss Neil Lennon will look for the same commitment from his players added to a cutting edge that was missing tonight.
There were surprises in both side's line-ups. Celtic's new signing Miku was handed his European debut for the Hoops as regular striker Gary Hooper, struggling with a knock sustained in the shock defeat at St Johnstone on Saturday, started on the bench.
Lennon reshuffled his side, bringing in Adam Matthews to right-back with Mikael Lustig moving into the centre of defence and Charlie Mulgrew starting on the left-hand side of midfield.
Benfica were without suspended skipper Luisao and Maxi Pereira while star striker Oscar Cardozo was among the substitutes with Eduardo Salvio, Nicolas Gaitan and Rodrigo making up the visitors' forward line.
It was another electrifying European night in the east end of Glasgow in front of a near capacity crowd.
Celtic midfielder Kris Commons, who was supporting Miku, showed his intent with two attempts on goal within the first couple of minutes, the first clearing the bar, the second blocked by a packed red and black defence.
Benfica looked unsettled as the home side chased and harried with the Celtic fans cheering every tackle, corner and throw-in won.
When the initial frenzy subsided the Portuguese side came into the game, forcing a couple of corners which came to nothing but signalled their growing confidence.
In the 21st minute Celtic midfielder Victor Wanyama was booked for preventing Enzo Perez racing towards the Hoops box after some neat inter-play from Jorge Jesus's men.
There was little goalmouth action at either end, though, until after the half-hour mark when Forster rushed from his goal to make a good block from Rodrigo who had raced on to a Perez pass which had opened up the Parkhead defence.
Emilio Izaguirre was then booked in the 34th minute for a lunge on Salvio and he almost cost his side dearly moments later when he was caught in possession by the same player, albeit he had been put under some pressure by skipper Scott Brown's pass, but the Benfica attack ended with the offside flag raised.
Benfica's lanky midfielder Nemanja Matic picked up a yellow card moments into the second half after catching Miku in the face while Lennon held his breath when Wanyama, already booked, pulled down Gaitan but referee Nicola Rizzoli showed some leniency.
The game swung end to end but the slackness from both sides, in terms of possession, seemed set to continue to the frustration of Lennon and his counterpart Jesus.
Benfica clearly fancied their chances as the second half unfolded further and just after the hour mark, following Pablo Aimar's whipped-in corner from the left, Forster made a good near-post save from Garay's header.
Benfica skipper Aimar was then replaced by Cardozo and Thomas Rogne came on for Lustig to partner Kelvin Wilson in central defence for Celtic before Izaguirre made way for Hooper.
The home side forced several corners in succession but failed to test keeper Artur while at the other end, in the 75th minute, Rogne had to throw himself to block Gaitan's goal-bound drive.
When Celtic broke from the corner, Commons tried to catch Artur out with a long punt from around the halfway line but the Benfica keeper scrambled back to save.
Inevitably the tension increased in the closing stages with the Hoops supporters knowing a goal would probably ensure the three points.
With 10 minutes remaining and Celtic pressing, winger James Forrest went down in the box when challenged by Benfica defender Melgarejo but referee Rizzoli stood firm in the face of vociferous appeals for a penalty, albeit it would perhaps have been soft if given.
In the 88th minute, as Benfica took another turn to search for a goal, Cardozo headed a cross from Andre Almeida over the bar from 12 yards but a winner then would probably have been cruel on Celtic.
