In reply, Bangladesh made a brisk start with a 44-run opening stand but could reach only 167 for six in their 20 overs.
Opening batsman Soumya Sarkar and Shakib Al Hasan scored 42 and 41 respectively for the touring side, who will next play two test matches in New Zealand starting on Thursday.
Bangladesh were 82-1 in the ninth over after the start provided by Tamim Iqbal (24) and Sarkar but the introduction of New Zealand leg-spinner Ish Sodhi (2-22) and other slow bowlers checked their progress.
Bangladesh paceman Rubel Hossain (3-31) dismissed James Neesham for 15 and Colin Munro for a duck in the same over before Mosaddek Hossain struck with his first ball to send back Tom Bruce (five).
Captain Williamson (60) then struck his second fifty of the series while left-hander Anderson provided the late assault during his 41-ball knock with the duo also bringing up the side's highest fourth-wicket stand in T20 internationals.
Anderson slammed part-time medium-pacer Sarkar for a hat-trick of sixes over mid-wicket, his 10 sixes the highest by a New Zealander in the T20 format.
(Reporting by Sudipto Ganguly in Mumbai; editing by Peter Rutherford)
