The Spain international struck twice in the first half to put his side in control against their third-tier opponents.
But the minnows, who have dumped out Villarreal, Racing Santander and Espanyol to reach this stage, gave themselves hope of yet another upset with a last-minute goal from substitute Ander Lambarri.
Mirandes coach Carlos Pouso predicted that next Tuesday's second-leg match at the San Mames stadium will not be easy for the Rojillos.
"We're going to have to play the match of our lives." the Spaniard said during a post-match press conference.
"It was clearly a game of two halves; we weren't able to do more. You couldn't help but notice our opponents were from the first (division)."
Fernando Llorente, who has netted eight goals under his name for the past six matches, has admitted that both teams were up to their necks during the match.
"The truth is it was a tough game," the 26-year-old striker said.
"We started well but that late goal is a shame because we'd played a good game until then."