The Glamour Boys entered the clash hoping to finish the season strongly and reach the 57-point mark for the first time since the Ernst Middendorp era.
However, a lack of sharpness in front of goal once again proved costly as the Soweto giants were punished by a disciplined Chippa side desperate to avoid relegation.
Despite the defeat, Amakhosi had already secured a third-place finish with 54 points and booked their place in next season's CAF Confederation Cup.
For Chippa, the victory was priceless as it lifted them to 13th place on the table with 28 points, enough to preserve their top-flight status.
Chiefs made an encouraging start and nearly opened the scoring just two minutes into the encounter. Debutant Naledi Hlongwane found himself with a golden opportunity inside the box, but the youngster failed to convert from close range.
The hosts continued to dominate possession for large periods of the first half, but struggled to break down a compact Chippa defence. The Chilli Boys remained patient and disciplined at the back while looking dangerous on the counterattack.
The visitors eventually made their moment count in the 33rd minute. Justice Figuareido spotted Sammy Seabi unmarked inside the area after the Chiefs defence switched off, and the defender calmly slotted home from close range to hand Chippa a crucial 1-0 lead.
Chiefs continued to enjoy most of the ball after conceding, but their attacking play lacked conviction as Chippa went into halftime with the advantage.
The hosts came out with renewed urgency after the break and nearly found an equaliser through Luke Baartman. Asavela Velebayi delivered an inviting cross into the area, but Chippa goalkeeper Dumisani Msibi reacted brilliantly to deny the striker.
Chippa offered little going forward in the second half but remained organised defensively. Figuareido nearly doubled the lead in the 64th minute after cutting in from the left, only for his effort to be blocked.
Chiefs continued to push late on, but poor decision-making in the final third frustrated their comeback attempts.
Their best chance arrived in the 83rd minute when substitute Tashreeq Morris found himself unmarked inside the six-yard box. However, instead of striking first time, the forward took an extra touch, allowing Chippa defenders to recover and clear the danger.
That missed opportunity summed up Chiefs' afternoon as Chippa held firm to secure the victory and survival on the final day of the season.