The Brazilians looked to be on their way to a third successive Absa Premiership win as Wayne Arendse fired home after 18 minutes at the Sisa Dukashe Stadium, but the defender turned villain before half-time, conceding the penalty which Rhulani Manzini smashed home.
Both Sundowns and Chippa enjoyed decent chances to snatch the three points in the second-half, but for some wayward finishing from the Brazilians and an excellent save from Wayne Sandilands to keep out Linda Shiba's close-range drive.
Speaking after the game, Mosimane seemed to have mixed emotions, telling SuperSportTV: "Both teams had chances, they had chances, but, under the circumstances, we will take a point because we [struggled] to play football.
"We played 'that' type of football, [with the ball] up in the air. That's not football. That's not good for Chippa, it's not good for Sundowns; we don't play percentage football.
"The rest... there's no football, it's a fight. That's not football."
The CAF Champions League-winning coach added: "I said before it's going to be a very tight game. We shouldn't be careless because the two sides were playing high-quality football so if [Chippa] score we might lose the game."
Speaking after picking up the man of the match award, Sundowns' January signing Fares Hachi said: "The congratulation is not for me, it's [for] team.
"It's good now, but [we look ahead] to the next match."