Sharks claimed their first United Rugby Championship victory by inflicting a first league defeat of the season on Ospreys.
A tentative first half saw two Gareth Anscombe penalties cancelled out by a pair of Boeta Chamberlain drop-goals.
Second-half tries followed from from centre Jeremy Ward and Marnus Potgieter before Chamberlain completed his drop-goal hat-trick.
Ruan Pienaar's two penalties saw Sharks score 21 second-half points.
Sharks shrugged off defeats by Munster and Glasgow while Ospreys had won their opening matches against Dragons and Cardiff.
Only wing Mat Protheroe offered any attacking intent against Sharks before he was brought off in the second half with a late Gareth Thomas try proving little consolation for an Ospreys side that made too many unforced errors.
Wales captain Alun Wyn Jones could not inspire his region when making his first Ospreys appearance of the season after captaining the British and Irish Lions in South Africa.
Fellow Lions lock Adam Beard had returned earlier than Jones with a couple of replacement appearances and also started against Sharks.
Centre Michael Collins and lock Bradley Davies were both missing through injury, while Wales prop Tomas Francis was a big loss after being a late withdrawal with a stomach bug with Tom Botha starting.
Anscombe opened the scoring with a penalty after Jones forced the mistake before Ruan Pienaar missed a long-range effort.
Pienaar intercepted a Webb pass before a length-of-the-field attack came to nothing, apart from a minor scuffle.
Anscombe doubled the score with his second penalty before Chamberlain levelled the scores with two drop-goals as the scores were 6-6 at half-time.
Sharks deservedly took the lead in the second-half through centre Ward after superb work from second-row Hyron Andrews, who collected a Chamberlain grubber kick.
Ospreys changed their front-row in an attempt to stop the Sharks forward and scrum dominance, but it had no immediate impact.
Sharks' confidence was rising and inevitably led to a second try for wing Potgieter after smart hands from the visiting backs.
A third Chamberlain drop-goal followed and his second direct from an Ospreys drop-out from their own line, while Pienaar added an extra three points.
Thomas' late Ospreys try never really threatened a dramatic comeback and a second Pienaar penalty settled Sharks nerves and completed the comfortable victory.
Ospreys head coach Toby Booth: "It was very disappointing, especially the nature of the performance to where we have been. We need to improve and improve quickly.
"We did not establish any field position and could not get out of our half. It was a typical South African pressure performance and we did not have any answers and that was the disappointing thing.
"We need to look at ourselves collectively and individually. We came second best tonight."
Ospreys: Dan Evans; Mat Protheroe, Tiaan Thomas Wheeler, Owen Watkin, Luke Morgan; Gareth Anscombe, Rhys Webb (capt); Nicky Smith, Sam Parry, Tom Botha, Adam Beard, Alun Wyn Jones, Will Griffiths, Jac Morgan, Morgan Morris.
Replacements: Elvis Taione, Gareth Thomas, Ma'afu Fia, Rhys Davies, Ethan Roots, Reuben Morgan-Williams, Stephen Myler, Joe Hawkins .
Sharks: Anthony Volmink; Marnus Potgieter, Jeremy Ward, Marius Louw, Thaakir Abrahams; Boeta Chamberlain, Ruan Pienaar; Ntuthuko Mchunu, Kerron van Vuuren, Thomas du Toit (capt), Ruben van Heerden, Hyron Andrews, James Venter, Gerbrandt Grobler, Henco Venter.
Replacements: Dan Jooste, Khwezi Mona, Lourens Adriaanse, Le Roux Roets, Phepsi Buthelezi, Dylan Richardson, Sanele Nohamba, Werner Kok.
Referee: Frank Murphy (IRFU)
Assistants: Craig Evans & Carwyn Williams (WRU)
TMO: Leo Colgan (IRFU)