The game started more than 30 minutes late due to heavy rain, but Downs soon got into their stride and took the lead on 24 minutes when through Eleazar Rodgers.
They looked to be heading for a win, but Tebogo Langerman put the ball past his own goalkeeper with just a few minutes to go.
Downs were slow starters and allowed Free State to control the play early on, which they did by creating a chance in the eighth minute when Dove Wome beat a couple defenders and took a shot from a tight angle, but Wayne Sandilands saved the shot.
That scare, however, was a wake-up call for Mosimane’s men and they began dictating the flow of the game, with Anthony Laffor in particular creating some havoc.
In the 14th minute Laffor supplied a beautiful pass from the right to see Teko Modise through on goal but, with only the keeper to beat, the midfielder seemed to kick the ground, resulting in his shot going wide from 14 yards out.
Ten minutes later and Laffor was in the thick of the action again; this time pressing down the left and making his way into the 18-yard box, drawing the keeper off his line before toe-poking the ball to an unmarked Rodgers, who beat one defender before firing home.
Stars had the final say in the dying seconds of the half; Moeketsi Mvula made use of some space down the right and burst into the box before unleashing his shot, but Sandilands saved again.
The second 45 was all Stars, but despite their dominant display they were not really able to create a decent chance. Instead they had to force the Sundowns defence into a mistake which resulted in them going level in the 73rd minute.
Stars whipped a teasing corner into the near post and Langerman, jumping in front of his keeper, accidently headed the ball into his own net.
Neither side could find the winner as the match ended all square which sees Downs remain second from bottom while Stars sit in sixth place.