It was a grinding, intense encounter in Madrid on Wednesday (Thursday AEST) between two clubs trying to return to the final after a long absence and looking to win the European title for the first time.
The match was in stark contrast to Tuesday's semi-final, when defending champions Paris Saint-Germain edged Bayern Munich 5-4 in a thriller in France.
Viktor Gyokeres put Arsenal ahead at the Metropolitano stadium by converting a 44th-minute penalty kick.
Julian Alvarez equalised for Atletico - also from the penalty spot - in the 56th minute.
Arsenal were awarded another penalty in the 78th minute after Eberechi Eze was brought down by David Hancko inside the area, but the call was overturned after a video review.
The second leg is next Tuesday in London. In the league phase of the competition, Arsenal routed Atletico 4-0 at the Emirates Stadium.
Atletico last made it to the Champions League final in 2016, when they lost to city rivals Real Madrid.
"We tried," Atletico midfielder Koke Resurreccion said.
"We had the opportunities to win, but it will all be decided in the second leg."
Gyokeres broke the deadlock on Wednesday from the penalty spot after he was brought down inside the area by Hancko, who was a bit late to the ball and slightly bumped the Arsenal striker from behind.
"Overall I think it was a tough game, we know it's a tough place to come, but it's only halftime," Gyokeres said.
"We know when we play at home, with our fans, it's going to be different for sure and we just have to do our job, be at our best, and for sure it's going to be a good game at home."
Arsenal last appeared in the final in 2006, when they lost to Barcelona.
Atletico's penalty came after a handball by Arsenal defender Ben White following a shot by Marcos Llorente. The call came after a video review.
Alvarez converted the penalty with a firm shot for his 10th Champions League goal this season.
The penalty was Arsenal's first attempt on target, but both teams had exchanged a few early chances. Arsenal goalkeeper David Raya had made a nice save on a shot by Alvarez, and Martin Odegaard had his dangerous strike from inside the area blocked by Atletico defenders.
Alvarez led the Atletico attack, but the connection with Antoine Griezmann and Ademola Lookman didn't work well until the second half.
Alvarez almost curled in a free kick strike after the break, and both Lookman and Griezmann had chances shortly afterwards.
Griezmann struck the post with a shot in the 63rd minute, and Lookman missed from close range later in the second half.
Many of the nearly 70,000 Atletico fans threw toilet paper from the stands before the match, creating a curtain of white paper.
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