Thabo Mnyamane made his first start since returning from injury, while Morgan Gould replaced Tefu Mashamaite in defence.
Eric Tinkler's charges enjoyed an encouraging start to the encounter as they managed to carve out a couple openings.
SuperSport had the ball in the back of the net in the 14th minute, but it was not given as a goal because striker Bradley Grobler had handled the ball.
The visitors managed to create a chance in 33rd minute, as they went in search of a crucial away goal. Fackson Kapumbu, however, fired his effort just wide of the upright.
ZESCO, who played Matsatsantsa's Tshwane rivals Mamelodi Sundowns in last year's CAF Champions League semi-final, ended the half on a stronger note, but they were unable to beat Ronwen Williams, who produced a save to deny Jesse Were just before the break.
The visitors should have opened the scoring shortly after the break, but Maybin Kalengo missed a sitter from cloe range.
ZESCO looked more threatening in the second stanza, but they were let down by their decision-making in the final third.
SuperSport were finding it tough to carve out chances, which prompted Eric Tinkler to introduce Dove Wome for Thabo Mnyamane for the final 20 minutes.
Williams was called into action on 80 minutes when he tippped John Ching'andu's long-range effort over the crossbar.
Both sides pushed for a winning goal in the closing stages, but they were unable to find the back of the net.
SuperSport: Williams, Kekana, Daniels, Gould, Modiba, Letsholonyane, Furman, Phala, Mnyamane, Grobler, Brockie.
Zesco: Banda, Silwimba, Owino, Musekwa, Kapumbu, Chaila, Mtonga, Daka, Ching'andu, Kalengo, Were.