Substitute Cele struck in optional time after Henrico Botes cancelled out David Zulu's opener for United before the break at Nelson Mandela Bay Stadium.
The home side were to draw first blood early on when Bafana Bafana marksman Zulu netted with an eighth minute penalty after Thulani Hlatshwayo had clashed with George Akpabio in the 18-yard area.
The goal spurred Gavin Hunt’s Clever Boys to life, with Chippa keeper Mbongeni Mzimela soon a busy man as the visitors piled on the pressure.
Mzimela kept his side’s lead intact as he saved from Jabu Shongwe on 17 minutes, before making an even better stop with a diving save on 28 minutes to deny Botes.
But the home defence was finally to cave in on 38 minutes when Gert Barends fouled Toriq Losper in the box, resulting in the second penalty of the game. Botes made no mistake as he beat Mzimela with the spot kick to restore parity after 40 minutes.
Moeneeb Josephs was the first goalkeeper called into action after the restart, the Clever Boys number one keeping Akpabio’s shot out of the net.
After that, with both sides not prepared to allow their opponents the upper-hand, the game remained tight and physical, the next chance on goal coming when Josephs saved from William Twala with 20 minutes to go.
Akpabio went wide with an effort in the 74th minute before Shongwe went even closer for the Gauteng side in the 87th minute.
With the clock moving towards full time, the spoils were seemingly about to be shared. But Chilli Boys captain Andile Mbenyane was determined to help his side to maximum points as he set up Cele to slot home the winning goal with one minute of regulation time remaining.