Ola John gave the Portuguese side an early lead before Giorgos Samaras equalised for Celtic, but Ezequiel Garay's 71st-minute winner left Celtic third in Group G and needing them to better Benfica's result in a fortnight if they are to advance to the knockout stage.
With Barcelona already through as group winners courtesy of a 3-0 win at Spartak Moscow earlier on Tuesday, a score draw for Celtic have would have secured them a berth in the next round, but Neil Lennon's side must now get a result at home to already-eliminated Spartak to keep their European hopes alive.
Lennon included Scott Brown, Joe Ledley and Gary Hooper in his starting line-up, despite initial concerns over their fitness, while Luisao returned for Benfica after serving a two-month suspension for pushing over a referee during a pre-season friendly in Germany.
Oscar Cardozo, making his first start in this season's competition, unleashed a long-range sighter that fizzed over Fraser Forster's crossbar inside the opening 60 seconds, but Benfica didn't have to wait long before breaking the deadlock.
Brown poked Eduardo Salvio's deflected cross away from Cardozo but straight into the path of Ola John, who powered a first-time strike beyond a helpless Forster to give Benfica the lead after seven minutes.
Paraguayan international Cardozo then spurned a chance to double the hosts' advantage as he could only find the side netting after drifting in behind Efe Ambrose.
But Samaras hauled Celtic level just after half an hour, rising at the far post to nod in Charlie Mulgrew's corner, a goal reminiscent of Victor Wanyama's opener against Barcelona two weeks ago.
The equaliser provoked a sustained period of attack from the Portuguese side with Kelvin Wilson making an excellent sliding intervention to deny Nemanja Matic before Forster stopped John from adding to his tally, sticking out a leg to turn the Dutchman's effort behind.
Lennon was forced into a defensive alteration with Beram Kayal replacing an unwell Mulgrew at half-time, and Brazilian striker Lima came close to breaching the Celtic backline on 53 minutes, escaping down the right and skipping past Andrews only to see his goalbound shot cleared off the line by Adam Matthews.
Luisao then demonstrated predatory instincts as he reacted quickest to Matic's knockdown header, only for the towering Brazilian centre-half to stab over the bar.
Lima squandered a glorious chance, failing to properly connect with John's cross, but Celtic eventually came unstuck on 71 minutes as Luisao nodded the ball towards an unmarked Garay, who drilled an unstoppable volley past Forster.
The visitors responded immediately with Wanyama and Kris Commons drawing a smart double save from Artur, but only the frame of the goal prevented the Scottish side from falling further behind as Salvio's dipping effort shook the bar.
Forster then made an acrobatic save to keep out a Cardozo free-kick before the England goalkeeper again had to be at his best to deny the Paraguayan for a second time.
Celtic also suffered another late blow as Wanyama collected a booking that rules him out of the next match, as Benfica held on to secure a deserved victory.