The Bhoys go down to defeat in Portugal despite a Georgios Samaras strike, with the second qualification place in Group G still up for grabs in the final round of matches
The home side went ahead early in the first half thanks to Ola John but the Bhoys found an equaliser despite having little of the play through Georgios Samaras' header.
The second period saw Benfica exert even more pressure on the away side, with Ezequiel Garay scoring the crucial goal in the 70th minute.
Benfica welcomed back Luisao into the centre of defence after his 11-game ban, while the highly rated Oscar Cardozo made his first Champions League start of the season. Meanwhile, Celtic made three changes from the side that beat Aberdeen, with Joe Ledley, Scott Brown and Gary Hooper all overcoming injuries to start.
The home side began the game confidently and took the lead in just the sixth minute as John pounced and drove the ball home after Celtic were unable to clear their lines.
Having gone behind, the Bhoys began to look somewhat nervous on the ball, struggling to keep possession and unable to create any clear openings of their own.
The home side were playing an attacking brand of football and came forward regularly but they struggled to break down a solid Celtic defence.
It took until the 29th minute for Benfica to create another chance, as Cardozo latched on to a through-ball and sent it wide with his left foot from six yards out.
Moments later, the away side were level, as a Charlie Mulgrew corner was headed home superbly at the back post by Samaras to give Celtic an equaliser.
However, despite some sustained pressure from the home side as they lay siege to the Scots' goal, the half-time whistle sounded with the scores level.
The second half began with some unfortunate news for Celtic, as Mulgrew was forced to be substituted at the break due to illness and was replaced by Beram Kayal.
The Bhoys were immediately on the back foot and had Adam Matthews to thank for keeping the scores level in the 52nd minute as he cleared Lima's shot off the line.
The away side were placed under a great deal of pressure by Benfica's attacking players, with Luisao shooting just over after a corner caused havoc in Celtic's penalty area.
The Bhoys were enjoying their best moments from set-pieces, with substitute Kris Commons showcasing some superb deliveries that were just about dealt with.
Benfica's pressure told in the 70th minute, howevber, as a knock-down from Luisao was powered home by Garay on the volley to recapture the lead.
Just three minutes later, the home side could have been out of sight but Salvio's superb dipping shot from outside the area struck the crossbar with Fraser Forster beaten.
However, with Victor Wanyama picking up a late booking meaning that he is suspended for the final group game away to Spartak Moscow, Celtic could not find an equaliser and were defeated.