Chasing 178 to win, Bangladesh were struggling at 102 for six but Akbar, who finished 43 not out, dragged them towards the line.
A brief flurry of rain saw the players leave the field with Bangladesh on 163 for seven. When they returned the target had been adjusted under DLS to 170 from 46 overs.
Bangladesh needed seven from 30 balls and Akbar and Rakibul Hasan duly knocked off the runs to claim Bangladesh’s first World Cup at any level.
“It’s an unbelievable experience,” said Rakibul who hit the winning run.
“We came here with plans and it worked out really well. Whichever team executes their plans better on the day wins, and that happened for us today.”
The day started well for Bangladesh when Akbar called correctly at the toss and put India in to bat.
Opener Yashasvi Jaiswal was again the stand-out batsman for defending champions India as he carved 88 from 121 balls.
The 18-year-old left-hander from Uttar Pradash already had three fifties and a century under his belt at this competition - the only time he failed to make a half-century was in the group match against Japan when India needed just 42 to win.
Jaiswal, who has just landed a contract with Indian Premier League side Rajasthan Royals, hit eight fours and a six before miscuing a short-arm pull off Shoriful Islam.
He ended the competition as top run-scorer with 400 at an average of 133.33 and was named Player of the Tournament.
Avishek Das was the most successful bowler with three for 40 and there were two each for Shoriful and Tanzim Hasan Sakib.
Tilak Varma made a watchful 38 from 65 balls and Dhruv Jurel 22 from 38 as the Indians struggled to attack the Bangladeshi bowling.
Jaiswal apart, the other Indian batsmen managed just four boundaries between them.
Bangladesh began confidently through Parvez Hossain Emon and Tanzid Hasan who brought up the 50 partnership with a six off Ravi Bishnoi. AFP