Antoine Griezmann and Rodrigo Riquelme's extra-time strikes earned Atletico Madrid a 4-2 win over rivals Real Madrid and passage to the Copa del Rey quarterfinals on Thursday.
Earlier Barcelona secured an unconvincing 3-1 win at third-tier Unionistas de Salamanca to scrape through their last-16 tie.
Atletico edged an entertaining battle at the Rojiblancos' Metropolitano stadium, the second of three Madrid derbies in under a month, to inflict Los Blancos' second defeat of the season in all competitions.
Madrid twice pegged back Atletico to take the game to extra-time, with Jan Oblak's own goal cancelling out Samuel Lino's opener, and Joselu netting late on after Morata had put the hosts in front again.
In extra-time Griezmann broke down the right and finished with aplomb and Riquelme struck at the death to settle the game and avenge Atletico's 5-3 defeat by Madrid in the Spanish Super Cup semifinal last week.
Defeat snapped Madrid's 21-match unbeaten run.
"I don't think (Atletico have the measure of us), because we beat them a few days ago," Real Madrid coach Carlo Ancelotti told reporters.
"We played a complete game, even, hard-fought, against a strong rival."
Once again, the match flowed end-to-end. Jude Bellingham hit the crossbar for Madrid before Atletico took the lead when Lino finished from close range.
However the Spanish Super Cup winners levelled before the break when Luka Modric's crossed free-kick drew Oblak out of his goal.
The Slovenian, leaping to reach the ball but unable to grab it, ended up getting the final touch as it span into his own net.
Real Madrid winger Vinicius Junior celebrated the equaliser more fiercely than anyone, with no love lost between the Brazilian and Atletico's supporters.
The home fans were jubilant early in the second half when Morata sent Atletico back ahead, after Madrid goalkeeper Andriy Lunin failed to gather the ball, and it fell invitingly into the striker's path.
Real Madrid hit the woodwork a second time through Rodrygo before Joselu equalised with 10 minutes to go.
After Vinicius slipped in Bellingham, the England international cleverly sliced the ball across for the target man to nod home and send the match to extra-time.
Griezmann cut through a tense first additional period with a brilliant solo run down the right wing, escaping Vinicius and finishing lethally across Lunin into the top corner to send Atletico ahead.
Substitute Dani Ceballos levelled for Madrid in the 111th minute but the goal was ruled out for offside, with Riquelme tucking home to settle the match.
"We had the patience to wait for our moment, Griezmann scored maybe his best goal and (Riquelme) finished well on the counter," said Atletico coach Diego Simeone.
Victory meant a lot to Atletico, off the pace in LaLiga and hurt by the prior Madrid defeat, and they celebrated wildly with their supporters.
"The games lately have been really nice for fans, at high speed, decided in extra-time and today it was our turn to win it," Atletico skipper Koke told TVE.
'SOMETIMES I DESPAIR'
After Alvaro Gomez brilliantly volleyed Unionistas in front, Spanish champions Barcelona clawed their way back to triumph with goals from Ferran Torres, Jules Kounde and Alejandro Balde.
After their thrashing by Madrid in the Super Cup final, the bare minimum they needed was to progress as doubts swirl around the club and coach Xavi Hernandez.
"We played well in parts, but in others we have to play better, sometimes I despair because we don't know what we need to," Xavi told reporters.
"When I say we're in construction, it's that, that we have to do what we need every single time."
The hosts, at their packed 6 000 capacity Reina Sofia stadium, were fired up and dreaming of an upset after already knocking out Villarreal.
Unionistas struck first to shock Barcelona with the unmarked Gomez volleying home superbly after 31 minutes.
Barca equalised before the break when Torres broke free on the counter, running through one-on-one from the halfway line, and kept his cool to finish well.
Xavi cut a frustrated figure until Kounde put Barcelona ahead with a bolt from the blue in the 69th minute, after being given too much time 25 yards out.
Balde made amends for his poor marking for the Unionistas goal by netting Barcelona's third, a superb solo strike.