Jaiswal was within sight of his second ton in the Border-Gavaskar series and Australia's Steve Smith was fearing the overtures of a Kohli batting masterclass.
The disastrous start to India's first innings, when captain Rohit Sharma's return to an opening role had only lasted three runs, was looking bearable.
It looked like only a run out could break the 102-run stand between Jaiswal (82) and Kohli (36).
They duly obliged, Jaiswal taking off for a rash single after driving straight to mid-on and his more senior partner having none of it.
Scott Boland had Kohli caught behind one run later, then had nightwatchman Akash Deep caught at leg gully for a duck, and from a robust 2-153, the tourists went to stumps in disarray at 5-164.
With the Border-Gavaskar series evenly poised at one-all and Australia posting 474 in their first innings, the last half hour on day two suddenly looks pivotal.
Kohli's dismissal came moments after his run-out debacle with Yashasvi Jaiswal. (James Ross/AAP PHOTOS)
"We looked like we were in a great position to get big runs ... but we will come back and continue to fight tomorrow morning," Indian allrounder Washington Sundar said.
"Definitely, (the) energy is very good in the dressing room, they're all positive.
"It's a long time in the game as well - still three days. It will just be about us trying to fight really hard and getting things done."
Earlier, former Australian captain Ricky Ponting had been scathing in his criticism after Rohit's dismissal.
The Indian skipper was cramped for room and skied his pull shot off Pat Cummins to Scott Boland at mid-wicket.
Out of form Indian senior statesman Sharma might not be long for Test match cricket. (James Ross/AAP PHOTOS)
"That is just a lazy, not switched on, not up for the moment type of shot," Ponting said on the Seven Network.
"He has been known as one of the best hookers and pullers of the ball since he made his debut, but that is just not there, it is nothing.
"It is not committed. It is not looking to be aggressive. He is just looking to tap it on the head.
"Might have held in the wicket, yes, might have seamed away from him a fraction, but if you are going to survive against this Australian attack you have to be switched on and making good decisions. If you are not, they will knock you over every time."
Yashasvi Jaiswal's 82 was at least one high point for India - before his calamitous run out. (James Ross/AAP PHOTOS)
The dismissal continued Rohit's bad run of form in the Border-Gavaskar series. After missing the first Test for family reasons, he has not scored more than 10 in four innings.
This is in stark contrast to Sam Konstas, Australia's youngest Test opener, who lit up day one with his audacious innings of 60 on debut and set the table for the home side.
And as the 19-year-old made the best-possible start to his Test career, there is speculation the 37-year-old Rohit might be on the verge of retiring from red-ball international cricket.
With this series tied 1-1, India rejigged their top order for Melbourne by dropping out-of-sorts No.3 Shubman Gill.
Rohit returned from No.6 to the top of the order and opened withJaiswal, as in-form KL Rahul moved down one place to take Gill's spot.
Adding to the potential implications of Rohit's cheap dismissal and the run-out calamity, Gill made way for Sundar - giving India a long tail for the fourth Test.
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