
Argentine striker Angel Correa put Atletico Madrid in front in the 62 minutes before Leonesa levelled seven minutes from the end through Julen Castaeda.
Sergio Benito then delivered the winner for the hosts in the second period of extra-time.
Partey was introduced at half time in place of Mexico international Hector Herrera.
The defeat completes a miserable January for Diego Simeone's Atletico who were defeated in the Spanish Super Cup by Real Madrid and 2-0 at Eibar in La Liga last weekend.
Atletico were one of four top-flight sides dumped out of the tournament on Thursday at the last 32 stage.
Also exiting the Copa del Rey on Thursday were Eibar, Real Betis and Celta Vigo. Read Full Story
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