"We are very happy to have won, it had been a long time without a victory against Barça," Carrasco said.
As well as the match, Barcelona also lost captain Gerard Piqué to a right-knee sprain early in the second half.
The win gave Atlético a nine-point advantage over Barcelona after eight matches. Diego Simeone's team is level with Real Sociedad at the top of the standings with 20 points and has a game in hand. Sociedad visits promoted Cádiz on Sunday.
Barcelona dropped to 10th place, staying with 11 points.
"The difference (of nine points) is pretty big," Barcelona coach Ronald Koeman said. "The league is still long and there are a lot of games left, but this defeat leaves us needing to string together a long run of wins"
Carrasco netted the winner after mistakes by both Piqué and goalkeeper Marc-André Ter Stegen. Piqué lost possession near midfield and Ter Stegen unsuccessfully came far out of his area to try to intercept a pass to Carrasco. The Belgium midfielder neatly slipped the ball between Ter Stegen's legs to set himself up for a shot from long range into the open net.
"It is worrying how we conceded the goal," Koeman said. "A big team cannot concede goal like that … We have (to) work more, especially in defense, to improve."
Atlético hadn't beaten Barcelona in the league since a 2-1 win in February 2010 at the now-demolished Vicente Calderón Stadium. The teams had played 20 matches since then, with Barcelona winning 14 times.
Barcelona had been the last team to beat Atlético at the Wanda Metropolitano Stadium in the Spanish capital, winning 1-0 last December in the Spanish league. Atlético is now unbeaten in 19 matches at the venue.
Atlético extended its unbeaten run in the league to 24 matches. Its last league loss was against city rival Real Madrid at the Santiago Bernabéu Stadium in February.
The game was supposed to be Luis Suárez's first match against Barcelona since being let go by Koeman and signing with Atlético. But he couldn't play after testing positive for COVID-19 while with Uruguay's national team. Newly signed Atlético midfielder Lucas Torreira also couldn't play after a positive test result with Uruguay.
Barcelona was without veteran midfielder Sergio Busquets because of a knee injury sustained while playing with Spain in the Nations League.
Piqué had to leave the match in the 63rd after Atlético forward Ángel Correa fell on his right leg. Piqué's knee bent inward and he had to be helped off the field. He struggled to walk and looked in a lot of pain, often putting his hands to his face.
Barcelona's Sergi Roberto also appeared to be injured when he left near the end of the match.
Barcelona started controlling possession but Atlético had the most dangerous chances early on. Ter Stegen saved well against Saúl Ñíguez's shot in the fifth minute, and Marcos Llorente hit the crossbar from close range in the 12th.
Lionel Messi put in a lackluster performance but had one of Barcelona's best chances in the 41st after a nice pass from Jordi Alba. The Argentina playmaker had his angled shot saved by Atlético goalkeeper Jan Oblak. Messi also missed from a free kick later in the second half.
Barcelona defender Clément Lenglet had his close-range header saved by Oblak early in the second half.
"We knew it was a difficult match here," Barcelona's Pedri said. "We didn't do well up front and they scored at the end of the first half, that was tough for us mentally."
