First half strikes from midfielders Pedro Munitis and Juan Carlos Valeron and a 30-metre thunderbolt from substitute Lionel Scaloni four minutes from time put the Galicians in firm control ahead of next week's second leg in Pamplona.
Valencia also look to be on course for a place in the last eight after claiming a valuable 2-0 win away to regional rivals Villarreal.
The visitors took the lead thanks to a superb individual goal by Mario Regueiro early in the second half, the Uruguayan winger rifling a shot low into the far corner after slipping his way past defender Javi Venta.
They took a comfortable two-goal advantage for the return leg at Mestalla when striker David Villa scored from the penalty spot after he had been felled by keeper Mariano Barbosa, who received his marching orders for his troubles.
Holders Real Betis had better luck than Osasuna on their visit to Galicia, coming from a goal down to earn a valuable 1-1 draw at Celta Vigo.
Celta took the lead when striker Jesus Perera converted from the spot after he went to ground under pressure from Betis defender Juanito midway through the first half.
But Fernando Vazquez's side were dealt a major blow when defender Jose Enrique was sent off for a reckless challenge on Dani just after the hour and Betis equalised when Matias Lequi fired a spectacular header into his own net as he tried to clear a cross 10 minutes from time.
The game of the night took place in Cadiz where the home side looked on course for a comfortable win over fellow Andalucians Sevilla after storming into a 3-0 before the hour was up.
KANOUTE DOUBLE
But two late headed goals from former Tottenham Hotspur striker Frederic Kanoute made the result 3-2 to Cadiz and put Sevilla right back in the tie.
Espanyol snatched a late 1-0 win away to Getafe courtesy of an 85th-minute header from Daniel Jarque.
Five minutes earlier Getafe strikers Daniel Guiza and Veljko Paunovic had spurned the chance to put their side ahead against Espanyol when they fired successive penalties over the bar.
Atletico Madrid's tie against Real Zaragoza was postponed after 14 members of the Atletico squad were laid low by gastro-enteritis during their training camp at the Spanish Football Federation's headquarters in Las Rozas.
Barcelona look certain to make the next round after coming from a goal down to claim a 3-1 win away to third division Zamora on Tuesday, while Real Madrid earned themselves a 1-0 victory at Athletic Bilbao.
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