Newcastle United came up short in their quest to take a step closer to a first trophy since 1969 as Eduardo Salvio's stoppage time strike stiffled a late Toon comeback at St James' Park.
After Tim Krul saved from Lima and Nicolas Gaitan in the first half, Papiss Cisse headed home with 19 minutes left as The Magpies sought to overturn a 3-1 deficit from the first leg.
But the hosts couldn't find a late winner despite substitute Shola Ameobi and Yohan Cabaye both going close as Jorge Jesus' side held out and when Salvio tucked home after Rodrigo's cross, the illustrious visitors' place in the semi-final was confirmed.
Alan Pardew was forced into four changes from the first leg in Portugal, with Massadio Hairdara starting for the first time since Callum McManaman's horror tackle on the Frenchman last month, while Mike Williamson and Gael Bigirimana began their first games since January.
Hatem Ben Arfa, with one appearance since December, returned after two spells out with a hamstring injury to a bench including Shola Ameobi and Sylvain Marveaux.
Oscar Cardozo, scorer of the third at the Estadio da Luz a week ago was the highest profile omission from a Benfica side which saw three changes as they sought to continue a 31-match unbeaten record and sustain their run to a first European final in 23 years.
The hosts were seeking to overturn history themselves; not least in reaching a first European semi-final for nine years, but becoming just the third side in Europa League history to overturn a two-goal deficit from the first leg against a side who had lost by two goals only once this season.
The visitors started from where they left off in the first leg with Lima, who scored the second goal in the first leg, testing Krul with a flick as early as the third minute.
The Dutchman was then forced to claw away Nicolas Gaitan's cross during a nervy opening from the hosts, whose defensive make-up only allowed for Papiss Cisse in attack and thus gifted the Portuguese league leaders constant invitations to launch to wave after wave of attacks in the opening exchanges.
And they almost grabbed a crucial away goal just before the half hour as Krul failed to gather from a long ball, allowing Lima to pull back for Gaitan, whose effort from point-blank range was hacked off the line by Haidara.
Salvio was then the latest Benfica played to miss the opportunity to add to the away side's advantage, as the Argentine headed wide from Ola John's cross.
Gael Bigirimana did manufacture Newcastle's first shot on target in the twilight of the first half, a dribble effort from the edge of the box but the rare opportunity only worked to emphasise the one-sided nature of the tie.
Cisse did have the ball in the net in the final minute of the first half but was ruled out for offside in the Senegalese forward's only moment of note in the first 45 minutes.
Ameobi replaced the ring-rusty Bigirimana at the break to beef up the Toon's attacking ranks and the move almost paid dividends within five minutes as the veteran forward, making his 51st European appearance, forced Artur into the turning the ball behind following his deflected drive.
Benfica continued to create openings however and after Gaitan again escaped Jonas Guitierrez Lima could only scoop his effort over the bar.
The introduction of Ben Arfa on 63 minutes produced the loudest cheer of the night from the home faithful, but those cheers were quickly muted as Cisse's had a second goal chalked off for offside.
But the ex-Freiburg forward soon had his goal as Ben Arfa and Ameobi chased down a lost cause in the right hand channel of the penalty area, with the latter crossing for Cisse to head into an empty net.
Krul saved brilliantly from both Gaitan and then substitute Cardozo, but as Newcastle pilled forward looking for a second goal they were caught on the break in the second minutes of added on time as Salvio found the middle of the goal to end the hosts' dreams of a place in the last four as rapidly turn their attention towards the tyne-wear derby this weekend.