Diego Costa's wonderful goal after 49 seconds, the fastest in Super Cup history, got Atletico off to a flyer in Tallinn on Wednesday.
But Karim Benzema headed in Gareth Bale's brilliant cross and Sergio Ramos converted a penalty awarded for a Juanfran handball to turn the tie around for Julen Lopetegui in his first game in charge of Madrid.
Despite Diego Simeone serving a touchline ban Atleti showed their fighting spirit to come from behind themselves, Costa scoring from close range before Saul's stunning strike in the 98th minute settled a gripping contest.
The brilliant Costa then combined with Vitolo to set up Koke for a drilled fourth that gave Atletico bragging rights over their rivals as well as the first European title of the season.
Atleti took the lead in the first minute of a thrilling clash, Costa rampaging away from Ramos and Raphael Varane to slam home past Keylor Navas after chasing down his own flick-on from Diego Godin's long ball.
Marco Asensio was close to equalising with a flicked finish from a Marcelo left-wing cross, but Jan Oblak made an excellent save.
Madrid equalised in the 27th minute, though, Bale delivering a wonderful deep cross from the right wing that Benzema nodded past Oblak.
With France forward Antoine Griezmann in muted form, Atletico gradually lost control of the contest and Madrid took the lead from the penalty spot after Juanfran handled in the area.
Ramos sent Oblak the wrong way from the penalty spot, scoring in the Super Cup for the second time and seemingly putting Madrid on course to win the trophy for the third year in a row.
But Marcelo's mistake on the touchline allowed Juanfran and Angel Correa to combine and set up Costa to slam home an equaliser in the 79th minute.
And when substitute Thomas Partey stood up a cross from the left, Saul was on hand to lash a vicious volley into Navas' top-right corner to regain the lead for Atletico, with Koke's fine first-time finish in the 104th minute wrapping up the scoring.
What does it mean: Atleti on track for title challenge
Atletico's key player Griezmann appears undercooked after firing France to glory at the World Cup, with the forward failing to record any touches in the Madrid box during his 57 minutes.
But victory for Atleti showed they are not as reliant on their talisman as they previously were. Thomas Lemar thrilled on his competitive debut, while goalscorers Koke and Saul were excellent in midfield. It is a second Super Cup for Simeone's side and a second LaLiga title could follow.
It hardly needs to be said that Madrid missed Cristiano Ronaldo. He is irreplaceable. But they must try.
Pat on the back: Saul stars again on European stage
The technique to volley in a Thomas cross was astonishing and the fight drifted out of Madrid after Atletico retook the lead in extra time.
Boot up the backside: Navas fails to make case for selection
When a new goalkeeper has just arrived, the last thing Navas needed to do was to concede a goal at his near post. Costa's finish was hit on the volley with a serious amount of power, but Navas had left an enticing gap.
Lopetegui showed faith in the Costa Rica international but within a minute there was proof it was misplaced and, while Navas could do little about the following three goals, Thibaut Courtois will surely be Madrid's number one this term despite not even making the bench in Tallinn.
LaLiga kicks off this weekend, with Lopetegui's return to domestic action coming at home to Getafe on Sunday. Atletico will welcome an extra day of rest after extra-time exertions - they travel to Valencia in a clash between two of the top four sides in the league last season on Monday.
Key Opta stats:
- Atletico Madrid are the first Europa League winners to go on to win the UEFA Super Cup since they themselves did so against Chelsea in 2012.
- Julen Lopetegui is the first Real Madrid manager to concede four or more goals in his first competitive game in charge since Michael Keeping against Celta Vigo in February 1948.
- Diego Costa scored his first brace in club competition since returning to Atletico Madrid, last doing so for Chelsea against Southampton in the Premier League in April 2017.
- Real Madrid’s Karim Benzema scored against Atletico Madrid for the first time since October 2015 in a La Liga match – he had gone eight games without finding the net against them.
- Sergio Ramos has now scored five goals against Atletico Madrid – only against Sevilla (six) has he scored more for Real Madrid. All five goals were scored in cup competitions (Copa del Rey x2, Champions League x2, UEFA Super Cup x1).