The Chilli Boys pressed the visitors in the first half as they looked to break the deadlock, but they could not beat Tshepo Ramaele in Tshakhuma goal.
The two teams were locked at 0-0 at the interval following a first half which was dominated by the home side.
An entertaining second half followed as Kurt Lentjies beat Ramaele to make it 1-0 to Chippa in the 52nd minute with Thabo Rakhale grabbing an assist.
Ndabayithethwa Ndlondlo was introduced by Tshakhuma as they searched for the equalising goal, but Chippa continued to launch attacks.
Lentijies, who was having a good match, turned provider when he set up Mark Mayambela and the latter hit the back of the net to seal Chippa's 2-0 victory in stoppage time.
Chippa's long-serving forward Andile Mbenyane was sent off in stoppage time for an off the ball incident.
Nevertheless, Chippa booked their place in the quarter-finals, while Tshakhuma bowed out of the tournament.
Meanwhile, Chippa's PSL rivals, Lamontville Golden Arrows travelled to Witbank where they were scheduled to face NFD club Witbank Spurs on Saturday afternoon.
It took only eight minutes for Lerato Lamola to put the visitors into the lead when he beat Spurs goalkeeper Edmore Sibanda to make it 1-0 to Arrows.
Nicknamed Siyavutha, Spurs pushed for the equalising goal, but the Abafana Bes'thende's defence stood firm at the back and the visitors were leading 1-0 at the interval.
Arrows managed to double their lead 17 minutes into the second half and it was Lamola, who grabbed his brace to make it 2-0 to the away side.
Spurs launched late attacks and they did pull one back in the 85th minute through Slovo Mrawu, but the goal proved to be a consolation goal as Arrows held on to win 2-1.
As a result, Arrows secured their place in the last eight, while Siyavutha crashed out of the competition.
The last game of the day was between an improving PSL side Bloemfontein Celtic and a stubborn NFD outfit Richards Bay at the Free State Stadium on Saturday night.
Celtic pushed for an early goal which would have unsettled the Richards Bay defence with the PSL's joint current top goalscorer Tshegofatso Mabaso spearheading the hosts' attack.
However, the Rich Boys were able to contain Phunya Sele Sele until the match referee blew the half-time whistle and the score was 0-0 at the interval.
Celtic pushed for the opening goal after the restart and they deservedly took the lead through Mabaso, who scored his ninth goal of the season to make it 1-0 to Celtic in the 66th minute.
Phunya Sele Sele were then awarded a penalty in the 70th minute, but Celtic captain Patrick Tignyemb was denied by fellow goalkeeper Andile Mbanjwa from the spot-kick.
Celtic then held on to their slender lead and they booked their place in the quarter-finals after securing a narrow 1-0 win over Richards Bay, who were eliminated from the tournament.