The hard-fought home win allowed the coastal side to move into the second spot on the South African Conference log with 15 points, three behind the Emirates Lions who won in Singapore earlier in the day, and one ahead of the DHL Stormers who lost in Wellington to the Hurricanes.
Only two points separated the two teams at the break with the Durban outfit 16-14 in front after the first 40 minutes of play.
The Cell C Sharks stepped up a gear in the second half to dot down two more times via flyhalf Robert du Preez and speedster Makazole Mapimpi, to add to the five pointer of Dan du Preez.
Well-worked tries by Tom English and Jack Maddocks brought the visitors to within two points of the home side, but they were unable to add to their tally in the second half mainly thanks to a fine defensive effort from the men in black.
Following a bright start to their campaign and then two successive losses, to the Vodacom Bulls and DHL Stormers, the Cell C Sharks gave a much more controlled attacking performance on their home turf.
Their powerful pack laid a good foundation for the backs to constantly trouble the Melbourne visitors and coach Robert du Preez will have been pleased with their overall performance.
Next up, the Cell C sharks host the Vodacom Bulls in another tough local derby, while the Rebels will face the Reds in their seventh round fixture.
Cell C Sharks 28 (16) - Tries: Daniel du Preez, Robert du Preez, Makazole Mapimpi; Conversions: Robert du Preez (2); Penalties: Robert Du Preez (3)
Rebels 14 (14) - Tries: Tom English, Jack Maddocks; Conversions: Quade Cooper (2).