PSL action continued on Sunday with the Brazilians cutting the gap between themselves and the log leaders
Themba Zwane and Thapelo Morena scored in either half for Sundowns while Dean Furman converted from the penalty spot in the second half but it was not enough to help SuperSport for a share of the spoils on the day.
It was a good recovery for Sundowns who had lost 1-0 to Orlando Pirates four days earlier.
With Chiefs dropping two points after being held 1-1 by Black Leopards on Saturday, Sundowns are now seven points behind the log leaders.
It was revenge for Sundowns over SuperSport who beat them 2-0 to lift the MTN8 Cup earlier this season.
Ndumiso Mabena scored for Celtic three minutes into the second half but William Twala responded for Chippa United eight minutes later.
The result saw Celtic remaining in seventh spot while Chippa are 10th on the log.
Ghanaian forward Mohammed Anas salvaged a point for Polokwane with a goal 20 minutes from full-time after Knox Mutizwa had thrust Arrows ahead eight minutes into the match.
With the point earned, Arrows moved to eighth on the standings but Polokwane are still on 17 points, the same as basement side AmaZulu.