After a dour first period, Racing opened the scoring with Sanz heading in a Pedro Orfila cross and Duran volleyed home with 12 minutes left to secure the victory.
It was reward for the battling spirit of the Racing players, many of whom have not been paid for several months while some have been transfer-listed as the club seeks to reduce its debts.
The problems at the club had boiled over during the first-leg of the tie when angry fans tried to storm the VIP tribune and remonstrate with club president Angel Lavin.
"Hopefully this isn't the last top flight side that we knock out. Now we will go for Villarreal or Real Sociedad (in the next round)," goalscorer Sanz told reporters.
"We need to keep working and enjoying the results. The situation at the club is making us stronger. We are a united group and we will fight against all the problems that we face."
(Writing by Tim Hanlon, Editing by Ken Ferris)
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