Olympiacos' 3-1 triumph over eight-man Anderlecht ensured that the Greeks claimed runners-up spot in Group C, while the Primeira Division side will have to be content with a spot in the Europa League.
It comes as a cruel blow to Jorge Jesus' men after they produced an excellent display against the Ligue 1 champions, recovering from Edinson Cavani's 37th-minute opener to claim the points on home soil.
But, despite inflicting PSG's first Champions League defeat in 14 matches, Benfica's inferior head-to-head record against Olympiacos saw their dreams of reaching the final, which will be hosted at their own ground, dashed.
Enzo Perez underlined Benfica's positive intent with an early long-range drive that forced a flying save from Salvatore Sirigu.
And Sirigu was called into action again with seven minutes on the clock, getting down low to his right to palm away Nemanja Matic's near-post effort.
It was the Portuguese side who carried the greater threat, however, and when Gaitan cut inside, he sent a curling left-footed effort just wide of the stranded Sirigu's right-hand upright as Benfica piled on the pressure.
But eight minutes before the interval, Blanc's charges took the lead as Menez raced to cut back a ball that appeared to be going out of play, with Cavani pouncing to turn home from point-blank range.
However, the response was swift, Lima converting from the spot following Traore's challenge on Silvio.
It should have been 2-1 to Benfica just two minutes into the second half but Gaitan shot woefully wide after Lima's blocked shot bounced to him eight yards out.
Jesus' men continued to press, the lively Lima testing Sirigu's reflexes again with a rising 20-yard strike after 52 minutes, and Luisao heading over two minutes later.
And they got their reward when Gaitan stabbed over the line from deep inside the area following excellent work from Maxi Pereira just before the hour mark.
