While Chiefs edged Pirates through a headed goal from Eric Mathoho on 81 minutes in Soweto, Sundowns suffered a shock 2-1 away loss to lowly Maritzburg after conceding an added-time penalty.
Peterson used his hands to push a rebound off the post up on to the underside of the crossbar and away to safety, then struck out a leg to foil another close-range attempt by Pirates to equalise.
Reeve Frosler broke the Premiership clash deadlock for Chiefs on 18 minutes with a fierce shot from just outside the box that goalkeeper Siyabonga Mpontshane got a hand to but could not keep out.
Ghanaian Kwame Peprah levelled on 54 minutes, tapping in a low cross at the far post for his fifth league goal of his first season in South Africa.
Veteran Mathoho outjumped two defenders to nod the match-winner and complete a league double this season for Chiefs over Pirates, whose rivalry is the greatest in South Africa.
Chiefs' victory and Sundowns' defeat offered a glimmer of hope that the climax of the 30-round season could be more exciting than feared.
Despite the setback, Sundowns hold a 16-point advantage over second-place Chiefs as they seek a record-extending fifth straight title.
But Chiefs have four matches in hand and will host Sundowns on May 8th as the most successful club in domestic competitions with 53 titles try to avoid going seven seasons without silverware.
Little went right for Sundowns seven days after a shock win over title-holders Al Ahly of Egypt in a CAF Champions League group match in Cairo.
Namibian Peter Shalulile gave the dominant local club in recent seasons a 37th-minute lead that lasted just four minutes before Alfred Ndengane equalised.
Sundowns' Themba Zwane had a second-half penalty saved by German Marcel Engelhardt before France-born Amadou Soukouna converted a 92nd-minute spot-kick for Maritzburg.
"Both Maritzburg goals should not have been allowed," insisted Sundowns co-coach Manqoba Mngqithi. "Ndengane committed a foul and Soukouna dived."