The hosts took the lead in the 36th minute when Jutgla's low pass across the goal found Sowah, who tapped tyjer ball into an empty net for his second European goal in three games.
Jutgla doubled the lead in the 62nd after winger Tajon Buchanan calmly waited for the right moment to set up the Spaniard inside the box.
Atletico had a chance to get back into the match with a penalty 15 minutes later but Antoine Griezmann lashed the ball against the bar and moments later the Frenchman thought he had scored but his effort was ruled out for offside.
"It was a good game," Atletico manager Diego Simeone said. "In the first half we played the game we wanted to play, we had two or three good chances. We weren't clinical and the first good chance they had, they took well. Then at the start of the second half Oblak made a good save, and after that their goalkeeper was key without doubt.
"I focus on the good things. There's a lot of Champions League left to play. We have to stay calm and know how to play the kind of games we have ahead."
Brugge, who have yet to concede a goal in the campaign, remain top of the group on nine points. Atletico, Bayer Leverkusen and FC Porto have three points each after Porto picked up their first points with a 2-0 win against the Germans.
Brugge and Atletico will face each other again next Wednesday in the reverse fixture in Madrid.
"It's practically [a final]," added Atletico midfielder Koke of next week's return match. "We'll have to win the three games we have left if we want to be in the round of 16."