After falling 2-0 down on the night, substitute Marcos Llorente struck twice in extra-time and Alvaro Morata added a late third to ensure a famous victory for Diego Simeone's side against a Liverpool team unbeaten in their last 25 home games in European competition.
Atletico midfielder Saul Niguez, however, criticised his side for not showing enough ambition early in the game.
All the action from football matches played in Europe on Wednesday
Real Madrid forward Vinicius Jr scored a hat-trick to help the LaLiga champions snap a two-game winless run in all competitions.
Real Madrid coach Carlo Ancelotti is looking for a big improvement from his side when they play their first home game of the LaLiga season, against Valladolid on Sunday, with Kylian Mbappe making his Santiago Bernabeu debut
First meets second as Barcelona host Atletico Madrid on Saturday looking to tighten their grip on the La Liga title race. The sides are level on 48 points at the top of the table, but Barca have a game in hand on Atletico and can take a huge step towards a fifth title in seven years with an eighth consecutive win in all competitions. Indeed, Luis Enrique's men remain on course for a repeat of the treble of La Liga, Champions League and Copa del Rey they won last season after progressing to the semi-finals of the Cup with a come from behind 3-1 win over Athletic Bilbao in midweek. Yet, the European champions have been far from their best in the past week as they were outplayed by Malaga and Bilbao in the first-half before being salvaged by individual moments of magic after the break. "We are aware of the errors we need to correct," said Luis Suarez after taking his tally for the season already to 30 with the equalizer against Bilbao.
Fernando Torres's head injury shocked his Atletico Madrid team mates as the striker had to be carried off on a stretcher towards the end of Thursday's 1-1 draw at Deportivo La Coruna.
Atletico Madrid's faint hopes of chasing down runaway Liga leaders Barcelona suffered a fresh blow on Saturday as they were held to a 1-1 draw at home to Girona, meaning they could fall 11 points behind the Catalans by the end of the weekend.
Real moved to 57 points, two ahead Girona and 10 clear of Atletico Madrid and Barcelona.
It was Messi's 30th goal in 39 competitive games against Atletico
In the dying minutes of their Champions League semi-final second leg against Real Madrid, a thunderstorm rolled in and drenched Atletico Madrid's Vicente Calderon stadium.
Diego Simeone has opened the door to the possibility of leaving Atletico Madrid in the next two years after announcing on Friday that he had reduced his contractual commitment from 2020 to 2018.
Atletico Madrid's problems deepened as they were held to a 0-0 draw at Villarreal in La Liga on Friday, stretching their winless run to four games in all competitions.
Atletico Madrid crashed out of the Copa del Rey to Girona on Wednesday following a highly entertaining 3-3 draw at home to the Catalan side, who sneaked through to the quarter-finals on away goals after the tie finished 4-4 on aggregate.
Atletico Madrid failed to build on Wednesday's notable Champions League success against Juventus when they were beaten 3-1 at a resurgent Valencia in La Liga on Saturday.
New Atletico striker Diego Costa, whose transfer from Chelsea was agreed this week, watched on from the stands as both sides hit the woodwork in the opening 20 minutes of an even first period.
If Atletico Madrid win a first Champions League title by beating city rivals Real Madrid on Saturday they will become the most successful team in the club's history, eclipsing the La Liga and King's Cup double winners of 1996.
Spanish prosecutors have won a series of cases against high profile footballers and coaches for tax fraud in recent years, including Lionel Messi, Cristiano Ronaldo and Jose Mourinho.
Runaway Premier League leaders Manchester City beat champions Chelsea 1-0 at the Etihad Stadium on Sunday to extend their lead to 18 points and leave the London side further adrift from the Champions League qualification spots.
The Kolkata-based franchise, partly owned by La Liga club Atletico de Madrid for the first three seasons, had earlier this month split from the Spanish club.
Manchester City came out on top in an epic Champions League battle against Monaco whereasAtletico Madrid beat hosts Bayer Leverkusen 4-2 in a topsy-turvy encounter.
Barcelona captain Lionel Messi scored two goals and set up two more as the Catalans thrashed Real Valladolid 5-1 to move top of La Liga on Tuesday.
Juve forward Cristiano Ronaldo had an unusually quiet game after scoring a hat-trick against Atletico in last year's competition, although he came within inches of grabbing a last-gasp winner when he sent a shot just past the far post.
'I haven't always expressed myself well. I said I would like to play with Neymar and Mbappe, but that doesn't mean I want to go to PSG'
News of all that's transpired on and off the football field
Atletico Madrid are not seeking revenge for their 2014 Champions League final defeat but instead want to write a new chapter in the club's history with their first European Cup after getting past Bayern Munich.
IMAGES from the UEFA Champions League matches played on Wednesday
Atletico Madrid substitute goalkeeper Antonio Adan saved three penalties before blasting home the winning spot-kick as the Europa League champions edged out Arsenal after the sides drew 1-1 in their International Champions Cup opener in Singapore on Thursday.
Arsenal manager Arsene Wenger was sad and frustrated after missing out on the Europa League final following Thursday's 1-0 defeat at Atletico Madrid in his last European game in charge of the London club.
Atletico Madrid tore apart city rivals Real Madrid 4-0 at home to open up the La Liga title race on Saturday in a triumph crowned by a spectacular overhead kick goal by Saul Niguez.
Atletico Madrid's troubles away from home continued when they were held to a goalless draw at Alaves on Saturday, dropping points on the road for a second consecutive week and losing Uruguay international Jose Maria Gimenez to injury.
Goalkeeper Ivan Provedel scored in the dying moments of the Champions League Group E match against Atletico Madrid, heading home the equaliser, to earn Lazio a 1-1 draw at Stadio Olimpico, in Rome, on Tuesday.
Images from the UEFA Champions League matches played on Tuesday.
The France striker was fouled by Leicester's Marc Albrighton on the edge of the box and referee Jonas Eriksson deemed the action to have continued into the penalty area.
Chelsea's Brazil left back Filipe Luis is poised to return to Atletico Madrid after one season at Chelsea where he failed to hold down a regular first team place, Atletico president Enrique Cerezo said.
Atletico Madrid coach Diego Simeone praised the 'decisive' Antoine Griezmann after his two goals helped down Olympique de Marseille 3-0 in the Europa League final on Wednesday and tried to convince the striker to resist the lure of Barcelona.
Manchester United showing 'concrete interest' in the French forward
"Our club has reached an agreement with Gelson Martins, making him a new Atletico player," said a statement from last season's La Liga runners-up.
Real Madrid manager Carlo Ancelotti said on Saturday he is happy with how new signing Kylian Mbappe is settling into life with the Spanish soccer giants and he has no concerns about his team's slow start to the LaLiga season.
The Catalonian side put up a good fight to stay level in the first half at a half-empty Wanda Metropolitano stadium, with Lucas Hernandez hitting the post and Diego Costa denied when one-on-one with the visiting keeper.
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