During his unbeaten 116-run knock, the left-handed opener combined with Mushfiqur Rahim (65) for a match-winning 118-run third wicket stand at the Sher-e-Bangla National Cricket Stadium in Mirpur.
Chasing 240 for the historic win, the Tigers, who beat Pakistan for the first time since 1999 in the opening match of the series on Friday, reached their target with 71 balls to spare.
The Tigers put up another fearless batting display right from the outset of the chase.
After Soumya Sarkar (17) fell early, caught behind off an edge off Junaid Khan, Tamim and Mahmudullah (17) set a blistering pace to the chase.
The duo raced to first 50 in 5.4 overs and reached 100 in 13.3 overs.
They clobbered 78 off 68 balls in the second-wicket partnership as Tamim blasted his fifty off 31 balls smashing 12 boundaries.
Mahmudullah went back soon after as Saeed Ajmal picked up his first wicket on his international return.
‘Run-machine’ Mushfiq, Friday’s centurion, was fluent from the start and a flurry of boundaries boosted the Tigers run-rate above six till the 32nd over.
Pakistan unsuccessfully reviewed an lbw shout on Mushfiq in the 24th over as the batsmen kept scoring runs with ease all round the ground.
After a floodlight issue halted play for about 15 minutes, Mushfiq reached his 22nd ODI fifty off 57 deliveries smashing six boundaries and a six.
The Tigers’ record partnership holders did not bank on boundaries only and rotated the strike regularly to keep the asking rate in check.
Tamim seemed to have lost some gas as Bangladesh edged closer to their target.
The 26-year-old opener, however, glanced Junaid down the leg-side for a boundary to bring up the fabulous ton.
Tamim brought up his sixth one-day international century from 108 balls and hit 17 boundaries and a six.
He also became the third Bangladeshi batsman to score successive hundreds after Shahriar Nafees and Mahmudullah.
After Rahat Ali sent Mushfiq back with the Tigers 22 runs shy of the win, Tamim fought his fatigue to bludgeon Junaid for a boundary and a six in the 38th over.
In the next over, Shakib Al Hasan worked a single behind square leg off Ajmal in the 39th over to bring up the winning run.
Pakistan’s new-look batting line-up again failed to fire.
Battling half-centuries from Saad Nasim and Wahab Riaz took them to a modest 239 for 6 in 50 overs after electing to bat first.
Nasim (77) fought a lone battle against a probing Bangladesh spin attack.
He paired with Haris Sohail (44) for a 77-run partnership before adding another 85 off 66 balls with Wahab (51), who lent fine support towards the end to take Pakistan to the score.
At one stage, Pakistan’s prospect of reaching 200 looked dim as the Tigers’ spinners put the tourists’ batsmen to the sword.
Pakistan were off to a cautious start after electing to bat first.
Sarfraz Ahmed (7) and Mohammad Hafeez (0) got out cheaply as the team stuttered to 37-2 in the powerplay.
Rubel Hossain struck in his first ball in the eighth over, taking out opener Sarfraz who flashed at an away-going delivery and was caught at wide slip by Soumya Sarkar.
The Tigers’ spinners then took the centre stage as Arafat Sunny sent Hafeez back for a duck in the next over.
New captain Azhar Ali made a patient 36 but he was caught behind off Shakib in the 16th over. Eight balls later, Fawad Alam went for a duck.
Shakib struck again trapping Mohammad Rizwan (13) in front to sink Pakistan further after Nasir Hossain skidded one through to crash into Fawad Alam’s middle stump. Pakistan were in big trouble slumping to 77 for 5 in 22 overs.