Sundowns, who won the reverse fixture 5-0 last week, needed a late winner from Hlompho Kekana to snipe the spoils in the rematch at Lucas Moripe Stadium on Wednesday night.
A third straight victory leaves Mosimane's side in fourth place on the table with 44 points from 22 fixtures - two points shy of leaders Cape Town City, and one behind Bidvest Wits and Kaizer Chiefs.
Downs and Wits have two games in hand on the Citizens and Chiefs, while SuperSport are now six points adrift of the summit.
Mosimane told SuperSport TV: "We squandered our games in hand, that is a fact and we are no longer there.
"Yeah, 1-0 and we go through again," he added, referring to the narrow defeat of Free State Stars on the weekend. "I'm happy to take 1-0, this is not a five tonight. It was a well organised SuperSport team, we probed, we tried to get through, it was not there.
"But I am happy with the boys, I am happy for the supporters, they've been patient with us, they keep singing, they kept us going."