Having disposed of La Liga clubs Villarreal, Racing Santander and Espanyol in previous rounds, the lowly club from Miranda de Ebro are dreaming of a final against Barcelona or Valencia.
However, they were rocked on their heels when Llorente netted his fifth goal in two games to put the visitors two ahead.
The burly Spain striker, who fired a hat-trick in Sunday's 3-2 La Liga win at Rayo Vallecano, nodded home a fine Oscar De Marcos centre for a 17th-minute lead.
The festive atmosphere on a chilly northern Spanish night at Mirandes's 6,000-capacity stadium dampened further when Llorente drilled a low shot into the bottom corner.
However, Mirandes, who have an annual budget of just over 1.2 million euros compared to Bilbao's of around 60 million, came out fighting in the second half and Hartiz Mujika clipped the top of the crossbar in the 64th minute.
Bilbao goalkeeper Gorka Iraizoz pulled off a brilliant save from Alvaro Corral's volley 15 minutes from time as the home side pressed forward.
"Conceding at the end was a shame as 2-0 would have been a great result but 2-1 is pretty good too," he told Spanish television.
"We really want to reward our fans with a trip to the final and let's see if we have luck in the return leg," he added.
Mirandes's unlikely cup exploits, only the second time a team from the Segunda B has reached the last four of the competition in its current format, have captured the imagination in Spain, where Barca and their even wealthier arch rivals Real Madrid dominate domestic competition.
Barca visit Valencia in Wednesday's second semi-final. Pep Guardiola's side, who disposed of holders Real in the quarter-finals, are without the injured Andres Iniesta and Pedro for the game at the Mestalla.
