Left-arm tweaker Jadeja found the edge of Smith's bat and bamboozled George Bailey, who was stumped.
Maxwell remained calm despite the dismissals of Shaun Marsh, Mitch Marsh and Matthew Wade that followed, guiding Australia from 3-150 to 6-295.
Maxwell skyed the ball and fell for 96 but James Faulkner completed the winning runs with seven balls remaining.
"It was a pretty amazing win," Maxwell said after being named man of the match.
"They scored a good score on a slow, low wicket. To chase that down with James Faulkner at the end is unbelievable.
"I feel like I've been making big strides over the last few months.
"The way I'm hitting the ball and approaching the game is different to what I've been doing over the last few years."
Maxwell smacked an unorthodox six when the victory equation blew out to 58 runs off 45 deliveries.
The tight finish tested the mettle of Maxwell and Faulkner, both short of time at the crease, but for the most part neither panicked.
One glaring exception came in the 45th over, when Maxwell was on 73 and took off for a single after clipping the ball to Umesh Yadav at square leg.
Yadav opted against having a shy at the stumps despite Maxwell being a long way out of the crease, much to the chagrin of India skipper MS Dhoni.
"It's tough to take. We didn't field well tonight," Dhoni said.
"There were at least three boundaries we should have easily stopped."
There was also more Decision Review System (DRS) angst for Dhoni - and many amongst a crowd of 47,638 that was predominantly India fans.
The visitors had a caught-behind appeal turned down when Maxwell was on 47, with the snickometer suggesting there had been a faint edge.
The result extended two impressive streaks.
Australia haven't lost a match in any format since an ODI against England on September 11 last year, while they're undefeated in ODIs at the MCG since March 2012.
However, the ease at which India continued to score raises further questions about the viability of Australia's inexperienced attack.
Kane Richardson boasted the impressive figures of 1-5 after his opening three overs, dismissing in-form batsman Rohit Sharma for six.
Kohli then took control of the contest despite four wickets to John Hastings.
Kohli moved past 7,000 ODI runs in his dig, setting a new world record by doing it in 161 innings.
The 27-year-old's malleable wrists were responsible for many of his runs, although a couple of heaved sixes off Scott Boland were all about power.
- AAP
