Benfica punished two second half mistakes from Davide Santon and Steven Taylor to score through Lima and Oscar Cardozo (penalty) after Papiss Cisse saw his early effort cancelled out in the first half by Rodrigo.
Cisse twice hit the woodwork for Newcastle as Benfica earned a two goal advantage to take into the second leg at St James' Park next week.
Benfica created their first chance of the game on nine minutes when Nicolas Gaitan fired in a dipping shot from 35 yards which was initially fumbled by Tim Krul before being gathered by the Newcastle keeper at the second attempt.
Newcastle broke the deadlock and grabbed a crucial away goal on 12 minutes when Danny Simpson's fantastic pass found Moussa Sissoko down the right and he crossed for Cisse to slot home from six yards out.
The visitors almost doubled their lead on 23 minutes when Cisse's shot from Jonas Gutierrez's cross deflected off Ezequiel Garay and hit the post before spinning into the grateful hands of Artur on the line.
Benfica drew level two minutes later as Krul could only push out Oscar Cardozo's powerful shot and former Bolton forward Rodrigo reacted quickest to smash the ball home from close-range.
Krul came to Newcastle's rescue soon after when he made a fine double save to deny Andre Gomes and Ola John from giving Benfica the lead.
Benfica were now on top and Krul was called into the action again to keep out efforts from Rodrigo and Nemanja Matic just before the break.
Newcastle almost restored the lead two minutes after the break when Marveaux sent Cisse clear on goal and the striker was unlucky to see his chipped effort over Artur come back off the post.
Newcastle gifted Benfica the lead on 65 minutes when Santon's backpass towards Krul was intercepted by Lima and he rounded the keeper before rolling the ball into the empty net.
Things got worse for Newcastle five minutes later when Taylor needlessly handled a cross into the box to give Benfica a penalty which Cardozo dispatched after being forced to take his spot-kick twice.