Holders Atletico were denied victory in their last-16 first leg at Valencia last week by Helder Postiga's injury-time equaliser.
But Raul Garcia's opener 17 minutes from time at Mestalla means Diego Simeone's side head into Tuesday's second leg at the Vicente Calderon with the edge on away goals.
Atletico are sure to be confident of securing a tie against either Real Betis or Athletic Bilbao, too, having beaten Valencia 3-0 at home in La Liga just last month.
Betis, meanwhile, travel to Bilbao on Wednesday with a narrow lead after Ruben Castro gave them a 1-0 win in last week's home leg.
La Liga champions Barcelona - who have won the Copa a record 26 times, most recently in 2012 - are all but assured of their place in the last eight after a comprehensive 4-0 first-leg win over Getafe at Camp Nou.
Barca were already well on their way to their fourth straight appearance in the quarter-finals thanks to a double from Cesc Fabregas before Lionel Messi - making his first appearance in two months after a hamstring injury - came off the bench to add a late brace of his own.
Gerardo Martino's men, who remain joint top of the league with Atletico following the sides' 0-0 draw on Saturday, overcame Getafe 5-2 away in the last game before the mid-season break, with Pedro scoring a hat-trick on that occasion.
A similar outcome this time around at the Coliseum Alfonso Perez would see Barca book a tie with Rayo Vallecano or Levante, who meet at the Estadio Ciudad de Valencia on Wednesday after playing out a 0-0 draw in their first leg.
Real Madrid are also well placed to reach the last eight after they eased to a 2-0 home win over Osasuna in their first leg, courtesy of goals from Karim Benzema and Jese.
Awaiting Carlo Ancelotti's team in the quarter-finals could be Segunda Division strugglers Alcorcon, who produced one of the biggest Copa shocks in history when they knocked Real out 4-1 on aggregate in the 2009-10 round of 32.
Alcorcon overcame the odds again in their last-16 first leg against Espanyol last week, with Dani Pacheco's late strike giving them a slender 1-0 lead to take to the Liga outfit on Wednesday.
Elsewhere, Villarreal will look to make home advantage count when they entertain in-form Real Sociedad - who are five games unbeaten in all competitions - on Thursday after claiming a 0-0 away draw last week.
The winners of that tie will play Almeria or Racing Santander, who meet on Tuesday after playing out a 1-1 draw in their first leg in Cantabria.
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