Chasing 251 for victory at the Shere Bangla National Stadium, the hosts cruised to their target with an unbeaten 127 from Sarkar and a fine 64 from his opening partner Tamim Iqbal.
Pakistan captain Azhar Ali (101) also hit a first ODI hundred but his young side imploded to be all out for 250 after losing their last eight wickets for 47 runs.
Azhar's century was the first in ODIs by a Pakistan captain since Shahid Afridi scored 124 in Dambulla in 2010 against the same opponents.
The 30-year-old, returning to the ODI fold after two years, added 91 for the first wicket with 19-year-old debutant Sami Aslam (45) and another 98 for the third with Haris Sohail (52) before being bowled by left-arm spinner Shakib Al Hasan's arm-ball in the 39th over.
In-form Tamim, who scored hundreds in the first two matches, continued his rich vein of form and the opening stand of 145 between the two left-handers put paid to any hopes that Pakistan had of avoiding another defeat.
Tamim fell leg before to left-arm paceman Junaid Khan but Sarkar continued to make hay, hitting 13 fours and six sixes, one of which took him from 95 to his first international ton.
Sarkar and former captain Mushfiqur Rahim (49 not out) breezed to the target with an unbroken stand of 97 for the third wicket from 70 balls to complete an emphatic win for the hosts.
Scoreboard:
Pakistan Innings
Az. Ali b Al Hasan 101
S. Aslam c Rahim b N Hossain 45
M. Hafeez b A. Sunny 4
H. Sohail c Rahim b Mortaza 52
M. Rizwan c&b Al Hasan 4
F. Alam c N Hossain b Mortaza 4
S. Nasim c Ahmed b R. Hossain 22
W. Riaz c Mortaza b R. Hossain 7
U. Gul run out (Al Hasan, A. Sunny) 0
Z. Babar not out 1
J. Khan b A. Sunny 4
Extras (lb-1 w-5) 6
Total (all out, 49 overs) 250
Fall of wickets: 1-91 S. Aslam, 2-105 M. Hafeez, 3-203 Az. Ali, 4-207 H. Sohail, 5-213 M. Rizwan, 6-224 F. Alam, 7-243 W. Riaz, 8-244 U. Gul, 9-245 S. Nasim, 10-250 J. Khan.
Bowling: M. Mortaza 10-0-44-2(w-2), T. Ahmed 2-0-22-0(w-2), Nas. Hossain 7-0-37-1, R. Hossain 6-0-43-2(w-1), A. Sunny 10-0-43-2, S. Al Hasan 10-0-34-2, Sa. Rahman 2-0-17-0
M. Mahmudullah 2-0-9-0.
Bangladesh Innings
T. Iqbal lbw b J. Khan 64
S. Sarkar not out 127
M. Mahmudullah b J. Khan 4
M. Rahim not out 49
Extras (lb-1 nb-2 w-4) 7
Total (for 2 wickets, 39.3 overs) 251
Fall of wickets: 1-145 T. Iqbal, 2-154 M. Mahmudullah
Did not bat: S. Al Hasan, S. Rahman, N. Hossain, M. Mortaza, A. Sunny, T. Ahmed, R. Hossain
Bowling: M. Hafeez 8-1-37-0, U. Gul 7-0-53-0(w-3), W. Riaz 6-0-30-0(w-1), J. Khan 7.3-0-67-2(nb-2), Z. Babar 10-0-56-0, Az. Ali 1-0-7-0.
Result: Bangladesh won by 8 wickets.
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