Eder's third goal in his last four games looked set to see Sampdoria leapfrog Rafael Benitez's men into third before Zapata stooped to nod home his second league goal of the season in the 92nd minute and earn his team a share of the spoils.
Kalidou Koulibaly was given his marching orders for Napoli in the 84th minute for picking up two yellow cards, but the visitors were not left to rue the 23-year-old's dismissal.
Faouzi Ghoulam steered a downward close-range header just wide in a rare early Napoli attack, while Eder had a 21st-minute effort correctly disallowed for offside after he had side-stepped advancing goalkeeper Rafael to net.
Koulibaly was cautioned for a crude challenge on Eder 10 minutes before half-time and the Brazilian was in the thick of the action once more when he broke the deadlock after 57 minutes with a fine goal.
Eder produced a decent turn and some nifty footwork to allow him to fire through a crowd a players and into the bottom corner from just outside the penalty area.
Gonzalo Higuain and Jose Callejon wasted half chances for Napoli before their hopes of getting back into the game were dealt a blow when Koulibaly left out a leg as Eder cut in from the wing to give referee Gianluca Rocchi no option but to brandish a second yellow and a red card.
Zapata, though, came to Napoli's rescue as he dived low to meet Ghoulam's looped cross on the edge of the six-yard box with a header that gave Sergio Romero no chance.
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