Ospreys' hopes of a first United Rugby Championship win in South Africa were thwarted as Sharks responded to their historic home defeat by Cardiff with victory in Durban.
Curwin Bosch's two penalties separated the sides in a scrappy opening period.
Luke Morgan finished a memorable Ospreys attack for the opening try and Sikhumbuzo Notshe replied for Sharks.
Morgan Morris crashed over to cut the deficit to a point, but late Bosch and James Venter tries sealed the home win.
The visitors were forced into late changes, with Wales scrum-half Rhys Webb and his initial replacement Reuben Morgan-William ruled out by illness.
Matthew Aubrey was brought in to start while shortly before kick-off, Michael Collins made way at centre for Tom Florence as illness again struck.
Wing Keelan Giles did start after being ill during the week.
Ospreys did not specify the nature of the illness afflicting their camp since their the bonus-point 43-26 defeat against high-flying Bulls.
Prop Rhys Henry and hooker Sam Parry came in, with Garyn Phillips and Scott Baldwin dropping to the bench.
Irish flanker Will Hickey, who made 15 tackles against Bulls without missing one on his URC debut, made his second successive Ospreys start.
Ospreys were also without Alex Cuthbert, George North, Joe Hawkins, Gareth Anscombe, Gareth Thomas, Adam Beard, Alun Wyn Jones, Jac Morgan, Justin Tipuric, Tomas Francis, Nicky Smith and Rhys Davies, who did not travel to South Africa having been in Wales' autumn squad.
In the previous round Sharks became the first South African team to lose to a Welsh region on home soil since the URC's expansion, as they were beaten 35-0 by Cardiff.
That defeat prompted the departure of coach Sean Everitt, with director of rugby Neil Powell stepping in until a permanent successor is named.
The Durban side made 10 changes, including the return of a number of players back from touring with South Africa, amongst them front-row forwards Ox Nche and Bongi Mbonambi, scrum-half Jaden Hendrikse and wing Makazole Mapimpi.
Bosch's boot proved the difference in the first half and though Mapimpi produced one blistering break, the visitors were more of a threat in attack - with Giles and Luke Morgan prominent - only to be denied as they were penalised at breakdowns.
Sharks' changes produced an improved forward effort, particularly at the scrums, but the first try fell to Ospreys early in the second half.
It was a superb team effort as Morris' burst from inside his own half and Giles' intervention set up the phase from which fly-half Jack Walsh's cross-kick found Morgan for the wing to go over.
Sharks' pack power brought the response for Notshe to touch down.
Morris hit back from a close-range drive, but Walsh could not convert from the touchline in the swirling wind.
After Bosch was well wide with a long-range penalty attempt, Sharks went for the line-out when awarded a penalty under Ospreys' posts.
The reward for that risk came as Bosch broke through for the decisive late try, which he also converted.
Venter then powered over to complete the win, with Bosch again adding the extras.
Sharks: Boeta Chamberlain; Marnus Potgieter, Francois Venter, Ben Tapuai, Makazole Mapimpi; Curwin Bosch, Jaden Hendrikse; Ox Nche, Bongi Mbonambi, Carlu Sadie, Vincent Tshituka, Gerbrandt Grobler, Sikhumbuzo Notshe, Jeandre Labuschagne, Phepsi Buthelezi (capt).
Replacements: Dan Jooste, Ntuthuko Mchunu, Khutha Mchunu, Hyron Andrews, James Venter, Grant Williams, Nevaldo Fleurs, Rohan Janse van Rensburg.
Ospreys: Max Nagy; Luke Morgan, Tom Florence, Tiaan Thomas-Wheeler, Keelan Giles; Jack Walsh, Matthew Aubrey; Rhys Henry, Sam Parry, Tom Botha, Bradley Davies (capt), Huw Sutton, Ethan Roots, Will Hickey, Morgan Morris.
Replacements: Scott Baldwin, Garyn Phillips, Ben Warren, Jack Regan, Harri Deaves, Matt Protheroe, Luke Scully, Cai Evans.
Referee: Eoghan Cross (IRFU)
Assistant referees: Stephan Geldenhuys & Griffin Colby (SARU)
TMO: Sam Grove-White (SRU)