Pakistan resumed their second innings needing a further 228 for victory with seven wickets in hand, but their chances faded when Olivier removed the dangerous Babar Azam (21) and captain Sarfraz Ahmed (0) in consecutive balls.
Aaron Finch's side will head to Sunday's decider in Hobart buoyed by Australia's first win in the short format since January and having delivered some badly needed cheer for the struggling cricket nation.
JP Duminy will captain a South Africa Twenty20 squad with three new caps to take on India in three matches later this month, Cricket South Africa announced on Tuesday.
Mohammed Shami produced a brilliant spell of reverse swing bowling to strike the mortal blows that earned India victory by 203 runs in the first Test.
Mayank Agarwal showed insatiable appetite for runs, converting his maiden Test hundred into a brilliant double before the Indian spinners tightened the noose around the exhausted South Africans on the second day of the first Test.
India displace SA off perch to become No 1 team in ODIs
Du Plessis will sit out the final match of the series starting in Johannesburg on Friday
IMAGES from Day 3 of the 3rd Test played between South Africa and India at the Wanderers stadium in Johannesburg on Friday
Pakistan's Shahid Afridi, on Monday, criticised the national selectors for resting six senior players, including skipper Sarfaraz Ahmed, for the upcoming ODI series against Australia, saying a good outing would have boosted their confidence ahead of the World Cup.
Dean Elgar scored an unbeaten century but an excellent spell of bowling from Australia seamer Pat Cummins restricted South Africa to 266 for eight at the close of play on the opening day of the third Test at Newlands on Thursday.
South Africa captain Faf du Plessis walked for the toss along with Temba Bavuma as the proxy captain, who was given the responsibility of calling the toss.
The 28-year-old Starc finished with a match haul of nine for 109, enabling him to overtake South Africa's new-ball bowlers Morne Morkel and Vernon Philander among others, eclipsing his previous best sixth position that he enjoyed in December 2016.
Lingerie giant Victoria's Secret's annual fashion extravaganza was held in New York.
Faf Du Plessis' injury prompted selectors to fast-track the 23 year old to the hot seat.
India will be desperately hoping that Rohit replicates his limited overs success in the traditional format
Pujara was placed sixth, down one rung, with 791 points, while Rahane occupied the ninth spot after slipping a couple of positions with 759 points.
After electing to bat, Sri Lanka were bowled out for 225, three balls short of their 50 overs, for another below-par score in a series where they have found no answer to South Africa's rampant pace and spin attack.
South Africa beat Sri Lanka by 87 runs
Fast bowler Kagiso Rabada took three wickets as South Africa bowled India out for 187 to take the opening day honours on a seaming wicket in the third and final Test at the Wanderers in Johannesburg on Wednesday.
Check out the Mumbai Indians squad for the eighth edition of the Indian Premier League.
IMAGES from Day 3 of the 3rd Test played between South Africa and Australia in Cape Town on Saturday
Fulfilling the quota requirements while fielding a competitive team has long been a sensitive issue but after a poor 2019, returning to winning ways looks to be the immediate priority of the four selectors, two of whom are black.
Opener Aiden Markram made a return to form as he scored 78 to help South Africa into a strong position on the opening day of the second Test against Pakistan at Newlands on Thursday.
South Africa can take inspiration from Sri Lanka's upset win over hosts England and string together victories to keep their slim World Cup hopes alive, batsman Aiden Markram said.
South Africa have named six uncapped players in their 17-man squad for the first two Tests of the four-match series against England as new coach Mark Boucher seeks to revive the fortunes of the ailing side. Batsmen Pieter Malan and Rassie van der Dussen, fast bowlers Dane Paterson and Beuran Hendricks, all-rounder Dwaine Pretorius and wicketkeeper Rudi Second will all hope to make their debuts in the first Test starting in Pretoria on December 26.
South African batsman JP Duminy is to return home ahead of the third Test against England in a move that could signal the end of his Test career.
Images from Sunday, Day 4 of the second Test between India and South Africa, in Pune.
South Africa have slipped to number six in the world, behind fifth-placed Sri Lanka, and have a host of questions to answer, not least around a brittle top six and the balance of the side.
IMAGES from Day 3 of the fourth Test between South Africa and Australia in Johannesburg on Sunday.
What happens when Victoria's Secret angels hang up their wings and get wicked...
Australia moved one wicket from victory in the first Test against South Africa on Sunday after Mitchell Starc's swing bowling decimated the hosts' lower order and dampened their hopes of an unlikely recovery.
Young pace sensation Lungi Ngidi has been rewarded for his recent performances with a place in South Africa's squad for the six-match ODI series against India starting in Durban on February 1.
South Africa must look to emulate England as they look to rebuild their squad and change their one-day international mentality following a premature exit from the World Cup, former all-rounder Jacques Kallis said.
Kohli made 160 not out from 159 balls as India, who had been put into bat, posted 303 for six in their 50 overs, before restricting their hosts to 179 all out to take a 3-0 lead in the series.
The India Under-19 team's World Cup title defence was dealt another blow on Wednesday when it suffered its second straight defeat in a warm-up game against South Africa, losing by five wickets, at the ICC Academy ground n Dubai.
With an unassailable 3-0 lead in hand, India need just one more win to claim their maiden ODI series triumph on South African soil.
South Africa built a sizeable second-innings lead after reaching 65 for two against India at the close on day two of the opening Test at Newlands on Saturday but were sweating over another potential injury blow for experienced seamer Dale Steyn.
They are new in the industry, but can give the seasoned models a run for their money.
South Africa bowled England out for 181 in their first innings and had built up a significant 175-run lead by the close of play on the second day of the first Test at Centurion Park on Friday. Images from Day 2 of the first Test between South Africa and England at Supersport Park in Centurion on Friday.
Ankit Bawne (46, 82), who looked set was out of the last delivery of the day, giving a return catch to pacer Junior Dala. India A require 255 runs on the final day with only four wickets in hand.
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