The Netherlands lit up the final day of Group 2 action when they dashed South Africa's semi-final hopes by pulling off a huge upset against Temba Bavuma's team.
Their 13-run victory sent India through to the semi-finals and injected fresh life into Pakistan's bid for a place in the last four.
India, who conclude their group campaign against Zimbabwe later on Sunday in Melbourne, and Pakistan are level on six points, while South Africa finished on five.
New Zealand and England have qualified for the semi-finals from Group 1.
Bangladesh began well after captain Shakib Al Hasan elected to bat and were 70-1 at the halfway stage.
Shadab Khan dismissed Soumya Sarkar and Shakib in successive deliveries though the lbw decision against the Bangladesh skipper, who had charged down the track, looked doubtful with replays showing an edge.
Najmul Hossain made 54 but Bangladesh could not make the most of the decent start and settled for a below-par 127-8.
Pakistan captain Babar Azam (25) and deputy Mohammad Rizwan (32) began cautiously but could not convert the starts and departed in successive overs.
Mohammad Haris produced a breezy 31 to calm nerves in the Pakistan camp as the 2009 champions went on to win with 11 balls to spare.
"We played pretty good cricket in the tournament," Pakistan fast bowler Shaheen Afridi told a new conference.
"Even the two matches we lost, those were in the final delivery. We did not get the results we wanted but there is no doubt that we played good cricket."
Earlier, South Africa, chasing 159 for a place in the semi-finals, managed 145-8 to crash out.
The Netherlands' top four batters made useful contribution to power the Dutch side to 158-4 after being put into bat at the Adelaide Oval.
Stephan Myburgh (37) and Max O'Dowd (29) gave them a decent start adding 58 runs for the opening stand.
Tom Cooper made 35 and Colin Ackermann chipped in with an unbeaten 41 to take them past the 150-mark.
South Africa struggled to get going in their reply losing both their openers - Quinton de Kock and Bavuma - inside the powerplay.
Brandon Glover, who claimed three wickets for nine runs, then scythed South Africa's middle order to set up a memorable victory for the Dutch side.
With the day's final match a dead rubber, India posted 186 for five after Rohit Sharma asked Zimbabwe to bowl first, with KL Rahul (51) and Suryakumar Yadav (61 not out) slogging seven sixes between them in a range-hitting clinic.
India's pacemen then routed Zimbabwe, who collapsed to 36 for five before being bowled out for 115 after 17.2 overs.
