Their win ended an agonizing title drought without the players even having to take the field after Chelsea beat Manchester City 2-1 at Stamford Bridge.
Atletico advanced 4-2 on aggregate in the round of 16, thanks to two goals by Marcos Llorente in extra time and another by fellow substitute Alvaro Morata.
Liverpool emerged from their recent mini-slump to get their Premier League title procession back on track with a 2-1 victory over Bournemouth at Anfield.
Klopp and his entire first team were all absent for the fourth round replay at Anfield as part of the club's winter break. The Liverpool manager was criticised for disrespecting the FA Cup, but his youngsters proved up to the task.
With a 4-0 win over Southampton on Saturday, Liverpool moved a scarcely believable 22 points clear in the Premier League, the biggest advantage any leader has had at the end of a day in English top-flight history.
The league leaders won the FIFA Club World Cup title last Saturday, take on second-placed Leicester City on Thursday and host Wolverhampton Wanderers on Sunday, but other teams including Manchester City are not as fortunate.
Thirteen-time winners Real Madrid were drawn against English champions Manchester City while title-holders Liverpool must face Diego Simeone's Atletico Madrid in the Champions League round of 16 following Monday's draw.
Liverpool and Arsenal both scored 5 goals, but a penalty shootout decided the match 5-4 in favour of Liverpool.
The match will be refereed by France's Stephanie Frappart, making Wednesday's Super Cup the first major men's European final to be refereed by a woman.
Liverpool opened its bid to end a 30-year English title drought by beating Norwich 4-1 on Friday, with four goals in the first half against the Premier League newcomers.
Liverpool will be seeking its sixth European title when it faces fellow English club Tottenham on Saturday in Madrid.
The Reds went into the match at Anfield trailing 3-0 from the first leg and deprived of injured star attacking duo Mohamed Salah and Roberto Firmino.
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