Negredo spot-kick puts Sevilla in cup command
Sevilla lifted the trophy in 2007 and 2010 and unlike many other La Liga teams in this round of a much-maligned competition, they fielded an almost full-strength side at the Sanchez Pizjuan.
Federico Fazio headed in a corner after three minutes and the visitors levelled in the 70th following a brilliant run and shot from Christian Alfonso.
Defender Cala bundled the ball in for the hosts from another corner in the 83rd minute before Espanyol full-back Ernesto Gallan was shown a second yellow card for a foul in the area and Spain striker Negredo netted from the spot.
"The best thing about the game is the result," Sevilla coach Michel told a news conference. "We can play much better than this."
La Liga sides Getafe and Valladolid also won but a clutch of top-flight sides lost to lower-league opposition including Osasuna, Real Sociedad and Levante.
Last season's runners-up Athletic Bilbao could only manage a 0-0 draw at neighbours Eibar of the Segunda B on a rain-soaked, churned-up pitch.
La Liga basement side Osasuna were beaten 1-0 at second tier Sporting Gijon after Gaston Sangoy netted in the 15th minute.
Sociedad went down 2-0 at second tier Cordoba while Europa League competitors Levante lost 1-0 at third tier Melilla who managed to hold on to their lead despite being reduced to 10 men near the end.
"Melilla were intense and more competitive," said Levante coach Juan Ignacio Martinez. "We need to make sure we never underestimate anyone and we must always keep our focus."
All three sides have the comfort of home advantage when they look to turn the ties around in the second legs scheduled for November 28.
Getafe thrashed second tier Ponferradina 4-0 with a double from Jaime Gavilan while Valladolid triumphed 1-0 at home to Real Betis thanks to a goal by Alberto Bueno just before half-time.
In Thursday's late game Manuel Pablo's fizzing long-distance volley for Deportivo La Coruna was cancelled out by Pedro Geromel's back-post header for Real Mallorca, leaving the sides level at 1-1 ahead of the return leg in Palma next month.