Ola John gave the home side the lead in the seventh minute before Georgios Samaras levelled in the 32nd minute from a Charlie Mulgrew corner.
Defender Ezequiel Garay restored Benfica's lead in the 72nd minute to ultimately, and deservedly, leave both sides on seven points after five games.
The Scottish champions, guaranteed a Europa League spot after Barcelona beat Spartak 3-0 in Moscow earlier in the evening, will go through if, in their home game against the Russian club, they better the Portuguese side's result in Barcelona.
While Neil Lennon can have no qualms about tonight's result he must fancy his side's chances of completing the job in front of a packed Parkhead against to a side who have nothing to play for, while Benfica, it must be assumed, will not be favourites in the Nou Camp.
A score draw would have been enough to take the Hoops into the last 16 while Benfica had to win to have any hope of qualifying.
The home side went into the game on the back of five clean sheets and knowing Celtic had failed to win away to the Eagles on three previous occasions and having failed to score in any of the games.
Celtic, buoyed by their incredible 2-1 home win over Barca earlier in the month, had skipper Scott Brown, midfielder Joe Ledley and striker Gary Hooper back in the side as Kris Commons, Beram Kayal and Tony Watt dropped to the bench.
Benfica captain Luisao was back for the first time in the group stage following an incident with a referee in a friendly against Fortuna Dusseldorf in August while midfielder Nemanja Matic returned after serving a one-game ban on match day four.
The home supporters in a less than full stadium were given early encouragement when striker Oscar Cardozo flashed a speculative shot from distance over the bar, after Samaras had lost possession in his own half.
It was a nervy start by the visitors and Benfica's opener came when Adam Matthews, playing at left-back, failed to clear his lines with a clearance, handing possession to Eduardo Salvio and when his cross arrived at John 16 yards out, he drilled his shot through the legs of right-back Mikael Lustig and past keeper Fraser Forster.
Mistakes and indecision peppered Celtic's play and on the half-hour mark they might have gone two behind when Salvio cleverly played in Oscar Cardozo but his drive went wide of the target.
Two minutes later, and out of the blue, Celtic were level when Mulgrew's in-swinging corner from the right was headed in by Samaras, strangely unmarked two yards out at the back post.
The goal immediately energised the Celtic players and as they moved forward with menace for the first time in the game and in the midst of driving rain the home side looked vulnerable.
Four minutes from the break, however, Salvio blazed a drive over the bar from the edge of the box after the Celtic defence had momentarily fallen asleep.
Moments later, with Benfica wresting control back, the Parkhead rearguard was again exposed but this time Forster blocked John's shot from 12 yards.
Kayal replaced Mulgrew for the start of the second-half but he was soon back peddling as Benfica came out with renewed vigour.
In the 53rd minute Matthews made up for his early error when he blocked a shot by Lima on the line, after the Benfica wide-man drifted easily inside past Hoops defender Efe Ambrose.
As the Eagles' pressure intensified, defender Luisao clipped the ball over the bar from five yards after the Celtic defence had failed to clear properly a John corner.
It was all hands to the pump for Celtic, who made another change in the 64th minute when Commons came on for Brown.
Forster was forced into another save from Lima's drive before Oscar Cardozo skimmed a header wide of the target.
In the 70th minute Salvio missed Lima's cross from the left when it looked like he must score but two minutes later that was forgotten when Matic's cross from the right was headed on by Luisao and Garay volleyed powerfully past the helpless Forster from eight yards.
As stunned Celtic wobbled, Salvio clipped the bar with a 25-yard drive before Forster tipped an Oscar Cardozo free-kick over the bar from the same distance, with the visitors surviving the corner.
Tension gripped the stadium in the closing stages with both sets of fans knowing the significance of a Celtic goal.
Two minutes from time Hoops substitute Watt, on for Ledley, had a drive from distance following a swift break easily saved by Artur.
But a minute later, as Benfica broke, Forster made a great save from Oscar Cardozo who had easily slipped the attention of Ambrose before sending in a drive from the edge of the box.
In the first minute of injury-time Kayal blasted a volley from 20 yards over the bar, and Watt drove wide from the edge of the box, ensuring that attention now turns to the final set of Group G fixtures in a fortnight, where more drama is guaranteed.
