Chasing 195, India needed 14 off the last over. Pandya smashed two sixes off Daniel Sams as India won with two balls to spare.
Starc left the team's bio-secure bubble in Sydney on Saturday after being told about a family illness.
Right-arm pacer Shardul Thakur was named as Jadeja's replacement.
Chasing a target of 162, the hosts could manage only 150/7. Leg-spinner Yuzvendra Chahal, who came on as a concussion substitute for Ravindra Jadeja, claimed 3/25, while debutant pacer T Natarajan took 3/30.
While Jadeja smashed an unbeaten 44 off 23 balls to propel India to 161/7, his head injury allowed India to unleash Chahal (3/25 in 4 overs) on an Australian side caught completely off-guard.
Malan and Morgan compiled a 51-run partnership to haul England back into the game after a career-best 3/19 spell for home spinner Tabraiz Shamsi had South Africa well placed to level the series.
Bairstow bludgeoned a brilliant unbeaten 86 from 48 balls as the tourists chased down 180 to beat South Africa by five wickets with four balls to spare on a slow wicket.
The design is an ode to the ancestors and past, present and future aboriginal cricketers.
Sushma Verma (34) and Sune Luus (37 not out) were main contributors in Velocity's successful chase.
The former fast bowler has served as an assistant coach with the Bangladesh men's team, and subsequently worked on a short term contract with the West Indies women's team, including at the World Cup 2020 held in Australia earlier this year.