The Magpies were rewarded for a lively start to the game when Papiss Cisse put them 1-0 up in the 12th minute, and the Senegal striker then hit the post.
Almost immediately after Benfica levelled through former Bolton forward Rodrigo, who fired in the rebound from a Tim Krul parry.
Cisse was denied by the goalframe again early in the second half as his delicate lob struck the upright, and then a terrible error by Davide Santon allowed Lima to put the hosts ahead.
Oscar Cardozo's 71st-minute penalty then made it 3-1 after Steven Taylor was penalised for a handball.
Although they were facing a team who had been beaten at home only once all season - by Barcelona - and netted more than 100 goals in the campaign, Newcastle boss Alan Pardew had indicated in the build-up to this fixture that he did not want his side simply to adopt a defensive approach at the Estadio da Luz.
And the Magpies showed their attacking intent from the word go, making a couple of early forays forward which saw Cisse send one shot into Artur's arms, then miscontrol in a good position after being played in by Sylvain Marveaux.
There was a scare for the visitors in the 10th minute when Krul, back in the team after seven games out due to an ankle problem, fumbled a Nicolas Gaitan strike, hastily gathering the ball at the second attempt with red shirts lurking.
Two minutes later, though, Newcastle were in front as Cisse met Moussa Sissoko's low delivery with a close-range tap-in.
Gaitan sent a header wide as Benfica looked for a response, but Newcastle then almost made it 2-0 as Cisse saw his deflected effort come back off the post in the 23rd minute.
Benfica made the most of that let-off, equalising within two minutes.
Krul did well to keep out a fierce Cardozo shot, but Rodrigo reacted quicker than any Newcastle defender and slammed the loose ball home.
Soon after, Benfica nearly completed a swift turnaround as Krul produced another fine parry, this time from an Andre Gomes attempt, and then kept out Ola John's follow-up with his feet.
Benfica kept up the pressure and Krul was again the saviour in the 36th minute as he kept out a snapshot inside the box from Rodrigo, who then flashed a further shot wide.
And Nemanja Matic was next to be denied by Krul, who saved the former Chelsea midfielder's header.
Newcastle went agonisingly close to regaining the lead two minutes after the restart when Cisse collected a pass from Marveaux and lofted the ball delightfully over Artur, only to see it hit the post once more.
At the other end, Cardozo stretched in the area in an effort to connect with Rodrigo's cross, but could not make good enough contact and the danger passed.
With it looking like anyone's game to seize, Newcastle shot themselves in the foot in the 65th minute as Santon, another to have returned to the side after an injury lay-off, made a mess of an attempted back-pass.
Benfica substitute Lima - who had come on for Rodrigo - latched on to the ball, rounded Krul and finished from a tight angle.
Soon after things got worse for Pardew's men, and again they ultimately orchestrated their own undoing.
A ball into the box hit Taylor's arm, referee Antony Gautier pointed to the spot and Cardozo converted the penalty - twice in the end, with him having to retake after Gautier ruled there had been encroachment as the first effort was struck.
Newcastle could find no response and will now have to produce something special in the return leg at St James' Park if their Europa League campaign is not to come to an end.
Source: Newcastle United Mad