The holders are now staring at a near impossible task in the return match.
Diego Simeone's side needed only 45 minutes at home to seize control of the tie, capitalising on a calamitous early error before carving Hansi Flick's team open at will to move to the brink of April's final in Seville.
Atletico took the lead in the sixth minute in extraordinary fashion.
Barcelona defender Eric Garcia rolled a routine pass back but goalkeeper Joan Garcia, already scanning upfield, allowed the ball to slip under his boot and towards goal. His desperate dive came too late as the ball had crossed the line.
Eight minutes later the lead was doubled with a flowing move. Ademola Lookman collected a long ball on the left and fed Julian Alvarez, who switched play to Nahuel Molina. The right back slipped a clever pass inside for Antoine Griezmann, who controlled smoothly and guided the ball into the bottom corner.
The third goal, in the 33rd minute, was another counter. Giuliano Simeone drove down the right and crossed low to Alvarez, who squared for an unmarked Lookman to fire into the bottom corner.
Flick reacted by sending on Robert Lewandowski in the 37th minute for Marc Casado. The change did little to stem the tide.
Instead, Atletico struck again before half-time. Lookman and Alvarez combined once more, the Englishman sliding a pass into the centre for the Argentine to unleash a strike into the top corner from just inside the box.
Barcelona dominated possession with 70 per cent in the first half, but it was Atletico's clinical transitions that did the damage.
Atletico goalkeeper Juan Musso denied Fermin Lopez early in the second half as Barca searched for a lifeline before the March 3 return leg at Camp Nou.
They thought they had one in the 52nd minute when Pau Cubarsi turned in a rebound from a free kick, only for the effort to be ruled out for offside after a lengthy VAR review lasting nearly six minutes.
Atletico remained dangerous and nearly added a fifth late on. Substitute Alex Baena was racing through unmarked in the 86th minute when Garcia brought him down from behind. The referee initially produced a yellow card but upgraded it to a straight red after consulting the pitchside monitor.
"It was crazy. Even more so against Barca," defender Marcos Llorente told Movistar Plus.
"The team did everything right. We stuck together at the back, we didn't sit back, we pressed high up the pitch, we broke up the space really well. Everything went our way."
The winners of the tie will face Real Sociedad or Athletic Bilbao in the final. Real Sociedad hold a 1-0 advantage ahead of their second leg in San Sebastian on March 4.
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