The left-arm spinner finished with four for 88 as Bangladesh, trailing by 459 runs, were bowled out for 275 in their second innings after lunch to suffer their 62nd defeat in 72 Tests.
Rehman, off-spinner Saeed Ajmal and paceman Aizaz Cheema shared five wickets that fell on a fourth-day track offering help to spinners after Bangladesh had resumed at 134 for four.
Fast bowler Rubel Hossain did not bat due a shoulder injury, suffered while fielding on Sunday.
Debutant Mohammed Nazimuddin (78), Shakib Al Hasan (51) and skipper Mushfiqur Rahim (49) were the main run-getters for Bangladesh.
Cheema ended the innings when he had Shahadat Hossain (21) caught by Umar Gul in the covers in his first over with the second new ball.
Rehman dismissed well-set Nazimuddin and former captain Shakib in the morning session before accounting for Rahim to finish the match with seven wickets after having taken three in the first innings.
Ajmal was the other wicket-taker in the morning when he bowled Mohammad Mahmudullah for no score.
Nazimuddin was involved in two stands, adding 78 runs for the fifth wicket with Shakib and 47 for the next with Rahim before being caught by Ajmal at mid-off. Opener Nazimuddin, 41 overnight, hit two sixes and nine fours in his 186-ball knock.
Nazimuddin, who was the second-highest scorer in the first innings with 31, defied the Pakistani attack for more than an hour and completed his half-century when he turned Rehman to deep mid-wicket for three.
Score board
BANGLADESH (I Innings): 135 all out
PAKISTAN (I Innings): 594/5 decl
BANGLADESH (II Inngs, O/n: 134/4):
Tamim b Hafeez 15
Nazimuddin c Ajmal b Rehman 78
Nafees lbw Ajmal 28
Ashraful c Hafeez b Rehman 0
N Hossain c Hafeez b Cheema 3
Shakib lbw Rehman 51
Rahim lbw Rehman 49
Mahmudullah b Ajmal 0
Sunny (not out) 20
S Hossain c Gul b Cheema 21
R Hossain did not bat (injured)
Extras (B-2, LB-5, NB-3) 10
Total (all out, 82.3 overs) 275
Fall of wickets: 1-24, 2-74, 3-75, 4-80, 5-158, 6-205, 7-210, 8-252, 9-275.
Bowling: Gul 13-2-45-0, Cheema 7.3-1-40-2, Hafeez 7-2-21-1, Ajmal 25-7-74-2, Rehman 30-7-88-4.
