Rohit, however, fell just eight runs short of a century, departing after a belligerent 41-ball 92 with seven boundaries and eight maximums as India made 212 for six after being put into bat first.
Australia made one change to the team that suffered a shock 21-run defeat by Afghanistan, with left-arm fast bowler Mitchell Starc replacing spinner Ashton Agar.
Shamsi claimed 3-27 in Sunday's three-wicket win over two-time champions West Indies as South Africa chalked up a seventh win in seven games at the tournament.
All four teams in Group 1 are still a mathematical chance to progress to the semi-finals heading into the final two matches.
If India win, they would move onto the semis with six points and Australia would remain on two points and their qualification hopes will be depend on the outcome of the Bangladesh-Afghanistan match the next day.
"To get that hat-trick in a place I was born, a place I played so much cricket, in front of my family, my friends, the atmosphere, hearing the music going and everything, a nice day," he said.
Cramped-up Glenn Maxwell's incredible double-century helped Australia snatch victory from the jaws of defeat in ICC 50-over World Cup in November, leading to Afghanistan falling just short of qualifying for the semi-finals.
A win for Australia would have sent the 2021 champions and India into the last four, but even a second hat-trick in as many matches from Pat Cummins was not enough to keep their unbeaten record at the tournament intact.
Bangladesh were the inferior side on display throughout the match and unsurprisingly suffered a 50-run drubbing.
Cramped-up Glenn Maxwell's incredible double-century helped Australia snatch victory from the jaws of defeat in ICC 50-over World Cup in November, leading to Afghanistan falling just short of qualifying for the semi-finals.
A win for Australia would have sent the 2021 champions and India into the last four, but even a second hat-trick in as many matches from Pat Cummins was not enough to keep their unbeaten record at the tournament intact.
Bangladesh were the inferior side on display throughout the match and unsurprisingly suffered a 50-run drubbing.
A string of attacking cameos powered India to 196 for five, their highest total in what has been a low-scoring tournament so far, in the Group 1 contest at the Sir Vivian Richards Stadium in North Sound, Antigua.
Cummins registered a hat-trick over two overs against Bangladesh on Thursday and the right-armer completed the feat once again against Afghanistan when he had Rashid Khan, Karim Janat and Gulbadin Naib dismissed with three consecutive deliveries.
Saturday's mauling was Bangladesh's second defeat in the Super Eights after an opening loss to Australia.
The left-handed opener is within touching distance of becoming the first Aussie to reach 1000 runs in T20 World Cups. Warner so far has scored 975 runs in 39 matches.
West Indies, tied with England on two points, rose to second place in Group Two thanks to a superior net run rate of 1.814. Third-placed England have a net run rate of 0.412, close to leaders South Africa (0.625) who have four points.
The match is scheduled to start from 8.30pm Bangladesh Time but the important Super Eight clash is likely to be affected by rain as the weather forecast for Antigua shows chances of thunderstorms.
Bangladesh are yet to win against India in T20 World Cups, having come up against the neighbouring country on four occasions in the mega event.
