The Brazilians, perhaps still suffering the effects of Absa Premiership title celebrations, were caught cold before even a minute played as Eric KwaKwa smashed a shot past Wayne Sandilands' near post after being teed up just outside the area.
Sundowns were the better team for the majority of the match but were not their fluid selves, their passing not as crisp, although they still created several chances to score.
Mzikayise Mashaba struck the woodwork from close range when it looked easier to score in the 33rd minute and Leonardo Castro also should have scored with his head from three yards out after a great pick-out by Keagan Dolly from the right side.
It didn't look like it was going to be Sundowns' day as chance after chance went wide or the wrong options were chosen, but Castro made up for his earlier miss with a headed goal from Dolly's corner-kick in the 81st minute.
The goal lifted the Brazilians and four minutes later it was 2-1 when Khama Billiat scored an outrageous goal from far out on the right flank. It looked like the Zimbabwean was trying to drill a cross to the far post for a runner but his strike sailed right over the goalkeeper and into the top-left corner.
Two minutes after that and Downs were cruising. After a set-piece, Thabo Nthethe squared for substitute Cuthbert Malajila to slot home and make it 3-1 with 87 minutes on the clock.
Sundowns play the second leg in Ghana on 17 May.
TEAMS
Sundowns: Sandilands, Mphahlele (S Zwane 73'), Nthethe, Arendse, Langerman (Modise 73'), Dolly, Kekana, Mashaba, Laffor (Malajila 49'), Billiat, Castro
Medeama: Tagoe, Adade, Amoah, Aidoo, Sarpong, Boahene, Kwakwa, Akowuah, Bio, Donsu, Abass Mohammed