Eduardo Salvio ended Newcastle's hopes of continuing their European adventure as Benfica struck deep into injury time to draw 1-1 and 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.
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 Gael 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.
The Magpies had 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.
Cisse was out of luck again 24 minutes from time when he converted Shola 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.
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.