The goals were scored by Knowledge Musona (brace) and Siphiwe Tshabalala for Chiefs, and Esau Mtsweni, Clifford Mulenga and Mpho Maleka for Aces.
Tshabalala's brilliant goal deep into injury time gave Chiefs a share of the spoils, in a game in which their slack defending almost saw them suffer their sixth defeat of the season.
Aces looked exciting at the start, and they pushed Chiefs to defend with their backs against the wall, with Clifford Mulenga, especially, causing problems for the visitors.
Aces were rewarded for their adventurous play with the opening goal in the 13th minute, when Lehumo Itshegetseng supplied Essau Mtshweni with a defence-splitting pass to the right wing, and the former Wits University midfielder unleashed a thunderous shot past hapless Chiefs goalkeeper Arthur Bartman.
However, their lead was short-lived as Chiefs drew level three minutes later when David Mathebula released Knowledge Musona with a good pass and the Zimbabwean striker beat Aces goalkeeper Thomas Richter with a low shot, despite attention from Aces captain and defender Felix Musasa.
Mulenga scored in the 29th minute as he found himself unmarked in a dangerous position and sent a long-range effort past Bartman for his fifth of the season.
As Chiefs' defence went to sleep again, defender Sepeke Manamela was allowed space to take a shot on the edge of the box that fell on the path of Mpho Maleka, who beat Bartman for his first goal of the season in the 36th minute.
Chiefs came out for the second half more lively, and were rewarded in the 55th minute when Musona registered his brace with a low shot, as he once again got the better of Musasa.
Chiefs pressed for the equaliser, with Abia Nale and Nkosinathi Nhleko coming close, but it was Tshabalala who, in the final moment, whacked a free-kick home in the 93th minute to break the hearts of Aces supporters.