Celtic's poor away record in the Champions League continued after they were floored by a late Benfica goal.
Benfica's Cardozo celebrates his late winner against Celtic
Both goalkeepers made saves to maintain parity in a poor first 45 minutes.
Benfica's Oscar Cardozo hit the woodwork twice in as many minutes in the second period as the home side ratcheted up the pressure.
And, just when it looked like Celtic would hold on, Cardozo popped up with four minutes left to claim victory for Benfica from close range.
Celtic had been given a pre-match boost with the news that captain Stephen McManus was able to start despite being knocked unconscious after a clash of heads in Saturday's Old Firm match.
John Kennedy, who came on as a substitute for McManus on Saturday, retained his place in defence.
Paul Hartley came in to play in front of the back four and Aiden McGeady was brought into the right side of midfield, as Shunsuke Nakamura and Evander Sno made way.
Celtic's Massimo Donati was left frustrated by Benfica's late goal
In attack, Kiwi Chris Killen was preferred to Scott McDonald as the lone front man in a cautious 4-1-4-1 formation.
Benfica had the lion's share of possession in the opening stages but were unable to carve out any concrete chances.
Kennedy and McManus in the Celtic defence were forced to head to safety on a number of occasions as the hosts launched crosses from the wide areas.
But Gordon Strachan's men were let off the hook in the 23rd minute, after McGeady's weak backward header was intercepted by Leo inside the box.
He hit the byeline and squared, only for striker Cardozo to miss the ball completely when he should have lashed home.
As the half wore on, Celtic, buoyed by a more composed performance than they have shown in recent away matches in the Champions League, started to venture forward.
Massimo Donati was the first to come close after 33 minutes.
Hartley targetted Killen with a free-kick into the box, his header across goal was met by the Italian who made Quim parry a solid strike from 12 yards.
Scott Brown then powered past three Benfica players and into the penalty area, only for Augustin Binya to track back and take the ball off the midfielder's toe.
And the same player watched a crisp drive from 20 yards fly just a yard wide of the post five minutes before the break.
But if not for Artur Boruc in the Celtic goal, the home side would have taken a lead into the break, when he stretched to tip a Konstantinos Katsouranis header over the bar.
The first-half clean sheet was a marked improvement on their visit to the Estadio da Luz last season, when they shipped two goals after 22 minutes.
The home side must have been given a rousing half-time speech by Jose Antonio Camacho as they came out fired up for the re-start.
Boruc was the hero again for the Parkhead side within just five minutes of the re-start, diving low to push away a powerful Cardozo header from point blank range.
Rui Costa then fired wide twice in quick succession as Benfica stepped up the pace.
The hosts' attacks created space at the other end and McGeady ghosted past Leo before stinging Quim's fingers from just inside the box but Celtic had to rely on the frame of the goal twice in two minutes.
Boruc could only push a Rodriguez pile-driver into the path of Cardozo, and the striker's shot rattled the underside of the cross bar from six yards.
Cardozo then watched a curled left-footed effort come agonising off the foot of the post.
With Celtic were under the cosh Strachan moved to bolster the midfield with Sno coming on for Donati.
McDonald replaced the increasingly-isolated Killen up front as Celtic tried to consolidate.
But just when it looked like Celtic would hold on for only their second ever away point in the Champions League, Cardozo beat the offside trap to chest down a through ball and lob over the advancing Boruc.
Benfica: Quim, Pereira, Luisao, Katsouranis, Leo, Nuno Assis (Di Maria 61), Binya, Rui Costa, Rodriguez (Luis Felipe 84), Bergessio (Adu 61), Cardozo. Subs Not Used: Butt, Edcarlos, Zoro, Ribeiro.
Booked: Di Maria.
Goals: Cardozo 87.
Celtic: Boruc, Caldwell, Kennedy, McManus, Naylor, Hartley, Jarosik, Scott Brown, Donati (Sno 63), McGeady, Killen (McDonald 74). Subs Not Used: Mark Brown, Balde, Nakamura, O'Brien, O'Dea.
Booked: McGeady, Killen, Hartley.
Ref: Massimo Busacca (Switzerland).