Chiefs suffered their first league loss of the season, from 12 matches, when Platinum Stars beat them 2-0 in Rustenburg on Saturday, while Pirates claimed a 2-0 win over Wits.
The two-time defending champions were now only a point behind their traditional rivals, after Chiefs had appeared to be running away with the league campaign.
Both Pirates and Chiefs will be without a game this weekend because of the Telkom Cup Final between Mamelodi Sundowns and Bloemfontein Celtic at Durban's Moses Mabhida Stadium on Saturday night, but the Soweto giants have one more Premiership match before December 8.