Youhana’s fourth century enabled the tourists to recover from 48-4 to reach 281-5 after electing to bat at the Bangabandhu National Stadium.
The total proved too big for Bangladesh, who could manage only 209-8 to lose the three-match series after their 49-run defeat in the opening match at Chittagong Tuesday.
The day-night match was held up for about half-an-hour after star Pakistani paceman Shoaib Akhtar had been hit on the head by an object from the stands during the Bangladeshi innings.
Akhtar was taken to the hospital for check-up and took no further part in the game.
It turned out to be a frustrating day for the Pakistani fast bowler, who conceded 45 runs in his opening five-over spell.
Tushar Imran top-scored with 65 for his maiden international half-century, hitting six fours in his 93-ball knock. He put on 51 for the third wicket with Al Sahariar (41).
Pakistan spinners Saqlain Mushtaq and Shahid Afridi did most of the damage, grabbing three wickets each in their disciplined spells.
The day belonged to Youhana, who put on 135 for the fifth wicket with Younis Khan (73) and 98 for the unbroken sixth wicket with all-rounder Abdur Razzaq (49) to steer his team to a big total.
Youhana struck 12 boundaries and two sixes in his 108-ball knock to surpass his previous best of 104 not out against the West Indies at Toronto in 1999.
The 27-year-old received valuable support from Younis, who hit five fours off 83 balls before being caught at deep mid-wicket while attempting a sweep off left-arm spinner Enamul Haque.
Pakistan, however, had got off to a poor start as they faltered against the Bangladeshi seamers.
Mohammad Sharif struck two early blows, while left-armer Manjural Islam and Khaled Mahmud took a wicket each to send the tourists struggling.
Opener Naved Latif went for a pull shot and was caught at deep fine-leg by Manjural off Sharif, while Afridi got the inside edge and was caught behind off Sharif.
Inzamam-ul-Haq also fell pulling, caught by Sanwar Hossain at mid-wicket, while Azhar Mahmood was stumped off first-change bowler Khaled Mahmud.
Pakistan and Bangladesh retained the sides that played the first match at Chittagong on Tuesday.
PAKISTAN:
Naved Latif c Manjural b Sharif 10
Shahid Afridi c K. Mashud b Sharif 4
Younis Khan c Javed b Enamul 73
Inzamam-ul-Haq c Sanwar b Manjural 3
A. Mahmood st K. Mashud b K. Mahmud 12
Yousuf Youhana not out 112
Abdur Razzaq not out 48
EXTRAS (LB-4, W-11, NB-4) 19
TOTAL (for five wkts, 50 overs) 281
FALL OF WKTS: 1-21, 2-23, 3-29, 4-48, 5-183.
DID NOT BAT: Rashid Latif, Waqar Younis, Saqlain Mushtaq, Shoaib Akhtar.
BOWLING: Manjural Islam 10-1-29-1 (2nb, 1w); Mohammad Sharif 10-2-59-2 (3w); Tareq Aziz Khan 9-2-56-0; Khaled Mahmud 10-1-50-1 (1nb, 1w); Enamul Hoque 10-0-69-1 (1nb, 4w); Mehrab Hossain 1-0-14-0.
BANGLADESH:
Javed Omar run out 12
Mehrab Hossain c Rashid b A. Razzaq 21
Al Sahariar b Saqlain 41
Tushar Imran c sub b Saqlain 65
Sanwar Hossain b Saqlain 5
Khaled Mahmud lbw b Shahid 12
Khaled Mashud lbw b Shahid 0
Enamul Hoque c Saqlain b Shahid 12
Mohammad Sharif not out 5
Tareq Aziz Khan not out 7
EXTRAS (LB-9, W-8, NB-12) 29
TOTAL (for eight wkts, 50 overs) 209
FALL OF WKTS: 1-16, 2-75, 3-126, 4-141, 5-179, 6-180, 7-193, 8-196.
DID NOT BAT: Manjural Islam.
BOWLING: Waqar Younis 6-2-10-0; Shoaib Akhtar 5-0-45-0 (5nb, 3w); Abdur Razzaq 8-1-36-1 (1w); Azhar Mahmood 7-0-29-0 (3nb, 1w); Saqlain Mushtaq 10-1-32-3 (1w); Naved Latif 5-0-25-0 (1w); Shahid Afridi 7-3-11-3 (1w); Inzamam-ul-Haq 2-0-12-0.
RESULT: Pakistan won by 72 runs.
UMPIRES: Showkatur Rahman and Syed Mahabub Ullah.
TV UMPIRE: Mahbubur Rahman.
MATCH REFEREE: B.F. Hastings (New Zealand).
MAN-OF-THE-MATCH: Yousuf Youhana.
FINAL MATCH: Dhaka (D/N), Friday.