Anamul scored a dominating 120 in Bangladesh's imposing 292-6 before spinners Abdur Razzak (3-19) and Sohag Gazi (3-21) dismissed the tourists for a low score of 132 in 31.1 overs in the second one-day for a 2-0 lead in the five-match series.
Bangladesh won Friday's first match by seven wickets, also in Khulna.
But the hosts took a giant leap on Sunday as they achieved their biggest one-day win, improving on their 146-run win over Scotland in Dhaka six years ago.
The West Indies were never in the hunt for the big target chase, losing wickets at regular intervals as the Bangladeshi spinners once again made stroke-play difficult for the batsmen on a slow Sheikh Abu Naser Stadium pitch.
Only Darren Bravo (28) and Kieron Pollard (25) offered some resistance as the top-order West Indian batsmen Chris Gayle (15), Marlon Samuels (16) and Lendl Simmons (nine) failed once more.
Gayle hit two boundaries and a six before edging paceman Mashrafe Mortaza to wicket-keeper Mushfiqur Rahim, while Simmons and Samuels were dismissed by Gazi who remained the best home bowler in Tests and one-days.
Bravo added 41 for the third wicket with Samuels before left-arm spinner Razzak struck thrice, dismissing Dwayne Smith (nought) in his second over and had Bravo and Devon Thomas (nought) in his fourth.
Earlier, it was the 19-year-old right-hander Anamul who in only his second one-day set up the win with a solid 174-run partnership with Rahim (79).
Anamul pulled a short ball from Ravi Rampaul in the 47th over to become the third youngest Bangladeshi and the eighth youngest in the world to score a century, behind countrymen Tamim Iqbal and Shakib Al Hasan.
Anamul faced 145 balls and hit 13 fours and two sixes, lifting the innings during a sixth wicket stand of 64 with Mominul Haque (31) as the hosts scored 86 in the last 10 overs.
The Anamul-Rahim stand is a new record for Bangladesh-West Indies one-days, beating the 146 between Ramnaresh Sarwan and Marlon Samuels in Dhaka 10 years ago.
It also becomes the highest total by Bangladesh in all one-days against the West Indies, improving on 276-7 they scored in Dominica three years ago.
Bangladesh had lost Tamim Iqbal (five) and Naeem Islam (six) by the seventh over but Anamul and Rahim repaired the innings.
Paceman Rampaul was the best among the tourists, finishing with a career-best 5-49.
The third match is in Dhaka on December 5.