Benfica's UEFA Champions League adventure came to end on Tuesday despite an excellent 2-1 win over Paris Saint-Germain.
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.
Lima levelled with a first-half spot-kick, awarded following what appeared to be an accidental clash of heads between debutant Kalifa Traore and Silvio, before Nicolas Gaitan struck the winner 13 minutes into the second half.
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.
PSG coach Laurent Blanc left Zlatan Ibrahimovic and Thiago Silva out of the squad altogether, with Cavani handed a starting berth.
The hosts featured Lima and Lazar Markovic in attack as Rodrigo, whose last-gasp goal earned the vital 3-2 triumph over Anderlecht last time out in the group stage, was named on the bench.
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.
The visitors fired a warning shot on the counter attack as Jeremy Menez raced down the left before seeing his low strike well kept out by Artur.
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.
Substitute Ezequiel Lavezzi almost grabbed an equaliser for PSG but saw his shot go just wide as Benfica held on for the win, only to be left disappointed by the news from Olympiacos.
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