After a goalless opening stanza, Downs ace Teko Modise opened the scoring with a curling strike from just inside the area in the 54th minute.
However, Lebese equalised in the 66th minute with a low, left-footed shot on the angle, after being teed up in the area by lively substitute Bernard Parker.
There were few clearcut chances in the opening stanza, as Kingston Nkhatha came closest when he ran onto Siphiwe Tshabalala's pass, but his shot was weak and straight at Kennedy Mweene.
Themba Zwane had a few long-range chances for Sundowns, while Modise came close towards the end of the half, but his shot went just wide.
The Brazilians, though, stole ahead when Modise beat Brilliant Khuzwayo with a delightful effort nine minutes into the second stanza.
Soon after Modise released Cuthbert Malajila but the big Zimbabwean put his effort over the cross bar.
Lebese then finished off an incisive team goal, with Tshabalala, Reneilwe Letsholonyane, Nkhatha and Parker all involved to earn a share of the spoils.