Benfica make the most of Newcastle mistakes
Hosts Benfica extended their Europa League winning streak to five having been behind to Cisse's 12th-minute opener and will take a precious advantage to the second leg at St James' Park next Thursday.
Newcastle put the home side under pressure early on and took the lead when Cisse connected with a pinpoint cross from French midfielder Moussa Sissoko.
Cisse was a constant threat to the Portuguese Premier League leaders, who had goalkeeper Artur to thank for a smart stop when he diverted the ball against the post from a shot by the Senegalese striker.
Instead it was Benfica who levelled through Rodrigo with just over half of the first 45 minutes gone, when the Spanish striker outpaced Newcastle's defence to pounce on a thumping shot from Oscar Cardozo that Newcastle keeper Tim Krul failed to hold.
Benfica coach Jorge Jesus was thrilled both for the result and the spectacle.
"What a great show that was for the fans. Speed in execution and movement from both sides. Shots hitting the woodwork, lots of misses and four goals," he told Portuguese radio.
"It was a Champions League quality game in my opinion."
Cisse should have put the visitors back in front when he found himself through on goal right after half-time but his clever chip hit the post.
Newcastle coach Alan Pardew lauded the striker's display.
"I thought his performance was outstanding. Not just for the goal, but the whole night he was a threat. He was unlucky not to come out with a couple of goals tonight," Pardew told reporters.
Benfica ruthlessly made the most of the visitors' mistakes in the second half when substitute Lima latched onto an underhit backpass from Davide Santon then dribbled around Krul and slid the ball home from a tight angle after 65 minutes.
The hosts dealt another blow to Newcastle six minutes later when Cardozo, ordered to retake his first penalty attempt, nervelessly converted from the spot after defender Steven Taylor handballed in the box.
Pardew still fancies his side's chances despite the defeat.
"I think we can put Benfica under pressure at home," he said. "Pressure can do funny things to you: could lose a player, you could score two quick goals and suddenly the tie is a very different feel."