The Magpies have work to do in the quarter-final second leg if they wish to advance after being put to the sword by Jorge Jesus's vibrant attacking side in Portugal
The visitors took the lead through Papiss Cisse, but were then pegged back by a Benfica side brimming with creativity. Goals from Lima and Oscar Cardozo after the break sealed the win after Rodrigo had equalised before half-time.
Newcastle made a positive start to the game as Cisse twice got in behind the Benfica defence, but on both occasions the Senegalese forward was thwarted by some instinctive defensive play from the home team's goalkeeper, Artur.
Pardew's side took a deserved lead in the 13th minute when Cisse made amends for his earlier missed chances by connecting well with Moussa Sissoko's sumptuous cross from the right to hammer the ball into the net.
And Newcastle then came close to adding a second when Artur adjusted his body brilliantly to tip a deflected effort from the Senegalese onto the post.
That Cisse chance seemed to spur Benfica into action, as they quickly equalised through Rodrigo. The Spaniard reacted quickest when Tim Krul parried Cardozo's dangerous shot, to poke the ball under the Newcastle goalkeeper and make it 1-1.
Jorge Jesus's side grew in confidence as the half wore on and were it not for a handful of great saves from Krul, could easily have gone in ahead at the interval. The Dutchman made fine stops from Nicolas Gaitan, Cardozo and Rodrgio before the end of the half.
Rodrigo in particular was proving a mischief for the home side, as he flittered between Newcastle's midfield and defence to initiate a number of his team’s most dangerous moves.
Newcastle started the second half in a similar vein to that of the first, as Cisse raced onto a tempting through ball from Sylvain Marveaux and lifted a delicate chip over Artur that flicked agonisingly off the post and away from danger.
However, the Eagles began to push forward as they sensed Newcastle tire and they went ahead in the 65th minute after a terrible back pass from Davide Santon. The Italian's wayward pass went straight to Lima and the Benfica substitute took the chance brilliantly by gliding past Krul and sweeping a shot into the net from a tight angle.
Within minutes the home side had made it 3-1 after they were awarded a penalty following a handball from Steven Taylor. Despite being made to take the spot kick twice by the referee, Cardozo showed great nerve to hammer the ball past Krul on both occasions.
Benfica looked the more likely to score in the closing stages of the game, as Newcastle struggled to create chances.
The result leaves Pardew's side with a big task on their hands when they welcome the Portuguese giants to St James' Park for the return leg on April 11.