Zesco broke the deadlock inside the five minutes when an un-marked Ching'andu volleyed home fine effort from close range.
Ching'andu nearly got his and ZESCO's second goal in the 13th minute, but Ronwen Williams produced a good save to deny the winger.
Eric Tinkler's charges started to see more of the ball as the half went on, but they were finding it tough to carve out chance.
SuperSport eventually leveled matters in the 35th minute when Thuso Phala drilled home a low effort from just inside the box.
Five minutes into the second half, Zesco restored their lead in the when David Owino peeled off his marker and fired home from six-yards out.
Tinkler opted for a change after 65 minutes as Thabo Mnyamane replaced Jeremy Brockie as they pushed for a third goal.
Zesco continued to push for more goals with Jesse Were proving to be real threat to the SuperSport defence.
Owin nearly got the home side's third in the 78th minute but his thumping header crashed against the crossbar with Williams well beaten.
However, SuperSport secured their spot in the final in stoppage time as Phala bagged his second of the game by firing home at the far post.
SuperSport: Williams, Kekana, Daniels, Gould, Modiba, Furman, Letsholonyane, Mokoena, Phala, Brockie, Grobler.