Holders Sevilla all but assured themselves of a place in the next round with a 4-0 hammering of Segunda B (third tier) Real Union, striker Alvaro Negredo scoring twice and Alejandro Alfaro and Jose Carlos weighing in with two more at the end.
The side they beat 2-0 in last May's final, Atletico Madrid, romped to a 5-0 victory at third-tier Universidad Las Palmas, when Argentina's Sergio Aguero scored two.
It was an evening of few upsets for the top-flight clubs, who have an advantage given that they play the second legs at home, meaning Racing will have a chance to turn things around in front of their own fans.
Valencia endured a tough first half away at third-tier Logrones but ran out comfortable 3-0 winners with a double from striker Aritz Aduriz.
Like La Liga leaders Real Madrid, who were held 0-0 at third-tier Real Murcia on Tuesday, Getafe and Villarreal also drew against lower league teams.
Getafe drew 1-1 at fourth tier Portugalete and Villarreal were held to the same scoreline at third-tier Poli Ejido, who levelled in the final minute.
Struggling Real Zaragoza edged second division leaders Real Betis 1-0 from the penalty spot, while Levante were also made to sweat, twice coming back to beat Xerez 3-2 with a late winner.
The last three ties of the round will be played on Thursday and the return legs in the week commencing November 8.
