Cisse could have had a second ten minutes later but his effort struck Ezequiel Garay before deflecting onto the woodwork.
That goal was the lifeline the Portuguese side needed to restore their power although they were dealt some luck when Cisse's chip immediately after the break also struck the post. From then it was all Benfica who forced Magpies keeper Krul to make a number of vital saves until they took the lead in the 65th minute.
Newcastle full-back Davide Santon produced a horror backpass which was pounced on by Lima who rounded Krul and slotted into an empty net.
Benfica's third goal came six minutes later when Magpies defender Steven Taylor inexplicably made contact with the ball with his hand, prompting a penalty. Cardozo was forced to re-take the spot-kick twice for encroachments but finally sent it past Krul for a handy two-goal advantage.
The return leg takes place at St James' Park next Thursday with Newcastle facing an uphill battle to reach the final four of the competition.
2012/13 Europa League quarter-final - first leg