Newcastle suffered a second-half collapse in their Europa League quarter-final first leg with Benfica. Papiss Cisse tapped in a low Moussa Sissoko cross as the visitors made the most of a bright start in Portugal.
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After Cisse struck the woodwork, the hosts came to life and Rodrigo pounced on a rebound to equalise for Benfica.
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Cisse hit the post again, before Lima punished a loose Davide Santon back-pass and Oscar Cardozo scored from the spot after a Steven Taylor handball.
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Newcastle had kept seven clean sheets in their previous 10 Europa League matches this season but, against Benfica, they were unable to set a club record of five successive clean sheets in Europe.
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Newcastle manager Alan Pardew has bemoaned the strain the Europa League had put on his squad as they continue to hover above the Premier League relegation places.
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The 51-year-old resisted the temptation to field a weakened side, however, and was even able to select Netherlands international goalkeeper Tim Krul after a seven-match absence with an ankle injury.
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They faced strong opponents in the Portuguese league leaders, who had already gone past the 100-goal mark in all competitions this season, and only been beaten at home by Spanish heavyweights Barcelona in the Champions League.
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But the visitors started the brighter in a rain-soaked Lisbon and went ahead when Cisse poked in at the back post for his 11th goal of the season after Sissoko burst free down the right flank and put in a perfect low cross.
Benfica did very good to beat Newcastle yesternite. The goals were magnificent cause they came at the right time