Morne Steyn played the first time since 2013 for the Pretoria side and his kicking boot gave the visitors a 9-6 halftime lead courtesy of two penalty goals and a trademark drop kick. The former Springbok flyhalf succeeded with two more penalties in the second half.
Springbok wing Sbu Nkosi scored the hosts' first try almost immediately after the break, while Curwin Bosch (flyhalf) contributed 13 points with the boot.
The first half was a tough arm wrestle between the two local rivals, with both sides conceding turnover ball at regular intervals.
However, the Durbanites edged ahead in the second half thanks to Nkosi's alert reaction to a pinpoint cross-kick from Bosch. Young replacement Nohamba then sealed the tie for the home side when he ran through to score next to the posts for a dramatic last-minute try on his debut.
Next week, the Cell C Sharks are away to the Highlanders while the Vodacom Bulls face the DHL Stormers in Cape Town.
Cell Sharks (6) 23 - Tries: Sbu Nkosi, Sanele Nohamba; Conversions: Curwin Bosch (2); Penalties: Bosch (3).
Vodacom Bulls (9) 15 - Penalties: Morne Steyn (4); Drop goal: Steyn.