The Swedish national team star won the penalty after being fouled by the home team's defender, David Hancko, at the end of the first half.
Gyökeres himself converted the penalty, blasting in the opening goal past home goalkeeper Jan Oblak.
The Swedish World Cup playoff hero had been out of Arsenal's starting XI in recent Premier League matches, but with Kai Havertz missing through injury he was given a chance.
It paid off; Gyökeres was substituted in the 68th minute.
The goal was Gyökeres' fifth in the Champions League this season - three of them have come against Atletico Madrid. The teams also met in the league last autumn.
But the Swede's penalty goal wasn't enough to secure victory.
The home team's Julián Alvarez equalized from the penalty spot in the 56th minute after Arsenal defender Ben White handled the ball.
Referee Danny Makkelie of the Netherlands awarded Arsenal another penalty in the 78th minute after Hancko brought down Eberechi Eze, but overturned his decision after a VAR review.
The return leg in London will be played next Tuesday.
In the second semi-final on Tuesday, Paris Saint-Germain beat Bayern Munich 5-4. The return leg will be played next Wednesday.
