Eduardo Salvio ended Newcastle's hopes of continuing their European adventure as Benfica struck deep into injury time to prevent another late show.
The Magpies were leading 1-0 on the night and pushing for the second goal which would have booked them a semi-final place when the midfielder slid home substitute Rodrigo's low cross to secure a 4-2 aggregate victory.
Papiss Cisse, who had earlier seen two efforts ruled out for offside, had set up a grandstand finish with a 71st-minute header, his fifth goal in seven games.
However, when the decisive moment came, it was at the wrong end for the home side.
Benfica, who started their European campaign in the Champions League, still have not lost in all competitions since October, although they came mightily close to doing so on Tyneside, and they will now head into the last four with ambitions of lifting the trophy.
Newcastle, who were applauded from the pitch by a crowd of 52,157, will now turn their attention to Sunday's derby clash with Sunderland.
Manager Alan Pardew chose his side with one eye on the derby match as Mike Williamson, starting his first game since January 19, was drafted into central defence and Massadio Haidara, back after escaping serious injury by Wigan striker Callum McManaman, Vurnon Anita and Gael Bigirimana got the nod.
Opposite number Jorge Jesus appeared so confident of defending a 3-1 first leg lead that he left dangerous frontmen Oscar Cardozo and Rodrigo sitting on the bench.
However, it was the visitors who dominated the opening 45 minutes as the anticipated Magpies assault failed to materialise.
They could have extended their lead within three minutes of the kick-off when Lima cleverly backheeled Andre Almeida's low cross towards goal, where goalkeeper Tim Krul made a vital block.
Cisse's control let him down with just keeper Artur to beat with 13 minutes gone when he ran on to Bigirimana's ball over the top - but Haidara came to the rescue with 28 minutes played when Krul came for a through-ball and perhaps fearing he was about the slide out of his area, allowed Lima to collect it. Lima unselfishly teed up Gaitan, but Haidara blocked on the line.
Krul was relieved to see Salvio head wide from Ola John's 36th-minute cross and then needed two attempts to collect Enzo Perez's dipping volley.
Newcastle did not muster their first on-target attempt until the final three minutes of the half, and Bigirimana's weak shot was not worthy of the combination between Yohan Cabaye and Moussa Sissoko which created the opportunity.
The Magpies did have the ball in the net in the final minute of the half when Cisse turned home Bigirimana's deep cross, although an offside flag correctly ruled out his effort.
Shola Ameobi's arrival in place of Bigirimana for the second half represented a show of intent by Pardew - however, John and Lima both fired wastefully over in quick succession as Newcastle went for broke and left Krul exposed.
Cabaye uncharacteristically wasted an inviting 57th-minute free-kick after Williamson had been tripped by Lima 20 yards out, but Gaitan was equally profligate when he side-footed wide from 18 yards six minutes later.
Hatem Ben Arfa joined the fray as Anita made way with time running out, and he saw his driven cross sliced wide of his own goal by Almeida.
Cisse was out of luck again 24 minutes from time when he converted Ameobi's flick-on, again from an offside position.
But it proved a case of third time lucky for the Senegal international with 19 minutes remaining when Ameobi's cross clipped Luisao and sat up nicely for him to head into the empty net.
The Newcastle bench were pleading in vain for a 75th-minute penalty after Cisse and Artur came together inside the box - but Croatian referee Ivan Bebek was unmoved.
Krul had to save twice from Gaitan as Benfica prospered in the space left by the home side as they pushed for a winner, with Salvio finally ending the home side's hopes when he tapped home from close range deep into injury-time.