Downs bagged a goal in either half in Puthaditjhaba on Wednesday night to hand Stars their first league defeat at home this season.
The visitors snatched the lead in the eighth minute through Surprise Moriri, who fired in a close-range strike after Tsholofelo Modise's free kick broke to him inside the 18-yard area.
Modise threatened again soon after but Stars goalkeeper Kennedy Mweene tipped his thunderous shot around the post.
The home side were made to sit back early but came close twice within a couple of minutes when first Ouro Sadate shot wide before Dove Wome blasted over the bar.
Both sides continued to create chances, and with 10 minutes left in the first half, Clayton Daniels and Wome fired wide.
Moriri missed his best chance for a brace minutes later when he connected with a Modise free kick, but Mweene held on to his close-range header.
Sundowns showed their intent immediately after the break, surging forward in an effort to stretch the gap, but Stars did well to threaten on the counter attack in an electric second half.
Five players -- Nyasha Mushekwi, Modise and Punch Manasamela for Downs, and Edward Mnqele and Wome for Stars -- wasted chances within 10 minutes after the restart, all firing wide or over the bar.
Mnqele was on target in the 54th minute when Wayne Sandilands was forced to parry away his effort, but Downs extended their advantage on the hour mark when Lebohang Mokoena connected with a cross from Modise and hit the back of the net.
Stars continued to fight and Mnqele had another opportunity with 13 minutes left but he blasted over the bar.
The hosts played with 10 men in the dying stages of the match, after Sadate was sent off with eight minutes left, and Zakari Morou fluffed their last chance when he fired a header over in injury time.
Sundowns take a three-point lead at the top of the standings ahead of a two-month break, with Stars dropping one place to sixth.