The tourists will attempt to bat for at least the remainder of day three at Optus Stadium after reaching 5-359 at tea, a lead of 405, in the first Border-Gavaskar Test.
With India in a commanding position, out-of-form superstar Virat Kohli (40 not out) was able to bat with freedom and spend some much-needed time in the middle.
As temperatures hover around a predicted 35 degrees, Kohli and allrounder Washington Sundar (14 not out) were looking to further wear down Australia's bowling attack after already spending 110 overs in the field.
Jaiswal has made life a hot and steamy misery for Australia, with 12 fours and three sixes. (Dean Lewins/AAP PHOTOS)
Kohli, who has scored just two centuries in almost five years, smashed a cut shot for six, with the ball then ricocheting off the boundary rope to hit an unsuspecting security guard in the head.
The guard was assessed by medical staff and taken from the field.
After being dismissed for a duck in the first innings in his first Test on Australian soil, Jaiswal scored a superb 161 to solidify his status as one of world cricket's rising superstars.
Starting Sunday unbeaten on 90, the 22-year-old quickly reached his fourth Test century when he ramped Josh Hazlewood over fine leg for six.
The left-hander triumphantly raised his hands in the air before hugging opening partner KL Rahul.
Nathan Lyon (left) and teammates weren't alone in their suffering, with a security man hit by a six. (Dean Lewins/AAP PHOTOS)
Jaiswal and Rahul (77), who was only recalled to the Indian team because captain Rohit Sharma was on parental leave, put on a 201-run stand - the highest opening partnership by an Indian pair in Australia.
The duo eclipsed the previous mark of 191, set by Sunil Gavaskar and Kris Srikkanth at the SCG in 1986.
Despite two Test centuries in India and another away to the struggling West Indies, doubts had lingered over how Jaiswal would perform in Australian conditions.
But he has excelled on a pace-friendly Perth pitch that has admittedly become easier for batting than when 17 wickets tumbled on a chaotic opening day.
Australia had their most productive session since early on day one when they took 4-84 after lunch, including a mini-collapse of 3-8 that featured Mitch Marsh's removal of Jaiswal.
Rahul played a strong support role to Jaiswal, contributing 77. (AP PHOTO)
With Australia heading towards their first Test defeat at Optus Stadium since it opened in 2018, and just their second overall in Perth against India, Pat Cummins' team will have to defy history.
The last time Australia recovered from a 1-0 deficit and came back to win a Test series was in the 1997 Ashes in England.
Australia last won a Border-Gavaskar series in 2014-15, with India holding the trophy since 2017.
This has been a stunning turnaround for India, who arrived in Australia fresh off a historic 3-0 home whitewash at the hands of New Zealand.
The Aussies were skittled for a woeful 104 in their first-innings, replying to India's 150, after stand-in captain Jasprit Bumrah (5-30) bowled superbly to enhance his already stellar reputation in Australia.
19°C