Rayudu stayed in the Indian XI in the second match and also played a role in the team's first two ODI wins in New Zealand.
England will not have to wait long for a chance of revenge, with the second test starting at North Sound on the island of Antigua on Thursday.
It was the largest margin of victory by the West Indies on home soil and third largest anywhere in their 91 years as a Test-playing nation.
England has set a tidy start but is still facing the daunting prospect of surviving two more days in Bridgetown.
The Men in Blue will return home to India triumphant without having lost a Test or limited-overs series -- a first on Australian soil.
Pakistan were 34 without loss at tea as they began the tough task of trying to chase down a massive target to try and avoid a clean sweep in the series.
Olivier broke through with the second ball after drinks when Abbas was caught at third slip for 11 after an 88-minute, 51-ball vigil.
It was only a fourth win in 20 one-dayers going back to June 2017 for world champions Australia.
The result ensured a seventh successive home series win for South Africa.
Marcus Harris, Marnus Labuschagne, Shaun Marsh and Travis Head were all dismissed in the second session, before captain Tim Paine followed shortly after the tea break.
South Africa won the first test in Pretoria last week by six wickets inside three days and are still strongly placed to clinch the three-match series.
Harris reaches his second Test 50 with a single off Jasprit Bumrah then smacked three fours in one Yadav over.
Paine acknowledges that not having world-class batsmen was hindering their chances of competing with teams like India, ranked number one in the world.
It leaves India zeroing in on a first-ever series win in Australia with just the Sydney Test next week to go.
The overwhelming victory gave New Zealand the series 1-0 after the first Test in Wellington was drawn.
India started with a 346-run lead and with five wickets in hand on a wearing pitch becoming increasingly difficult to bat on.
Arthur stormed into third umpire Joel Wilson's room and questioned him.
Paine said he was not annoyed "in the slightest" by Kohli looking straight past him at the handshake.
Finch's right index finger suffered a nasty blow when during the second test in Perth, forcing him to retire hurt.
The hosts led by 43 after both teams' first innings despite a superb Virat Kohli century, but found batting incredibly tough in their second innings.
The imperious Kohli was unbeaten on 82 and shaping as the major stumbling block for Australia.
Southee claimed three wickets in his first two overs as the Black Caps' decision to bowl on a green Basin Reserve wicket after winning the toss paid immediate dividends.
Ashwin is receiving treatment for a left-sided abdominal strain, while Sharma jarred his back while fielding in Adelaide.
The only successful fourth innings Test run chase of more than 300 at Adelaide came in 1902, when the hosts made 315 to beat England.