Having made 262 for seven in their 50 overs, Pakistan restricted Bangladesh to 186-7 in Dhaka to notch their record sixth consecutive one-day international series win.
Nasir, playing his ninth one-dayer for Bangladesh, came to the crease when the hosts were reeling at 19-4 and survived two dropped catches on nought and nine before being caught off Umar Gul for 100 in the final over.
The 20-year-old, who hit 11 fours and a six, added 106 runs with former skipper Shakib Al Hasan (34) for the fifth wicket to help Bangladesh avoid more humiliation.
Gul finished with figures of 4-36, including a two-wicket burst in the final over.
Pakistan are unbeaten in a bilateral one-day series in 2011, despite ongoing problems, which have included a spot-fixing scandal and the absence of international cricket in the country because of security concerns.
They secured series wins over New Zealand 3-2, West Indies 3-2, Ireland 2-0, Zimbabwe 3-0 and Sri Lanka 4-1.
Pakistan won five successive series from March 1989 to December 1990 under captain Imran Khan before Waqar Younis and Inzamam-ul-Haq led them to the same feat in 2002.
Umar Akmal, who added 83 runs with Misbah for the fourth wicket, made Pakistan’s only half-century before he was caught by Shafiul Islam off Shakib Al Hasan for 59.
Shaid Afridi was dropped by Shafiul on eight and went on to reach 42 off 27 balls with three fours and two sixes.
