New Zealand were 275 for three midway between lunch and tea on the fourth day to lead Bangladesh by 64 on the first innings.
Despite the discomfort, Williamson made 74 before he was dismissed.
Starting off the day on 38/2, Taylor and New Zealand captain Kane Williamson converted their 30-run partnership into a 172-run stand, during which both batsmen surged past their fifties, before Williamson was caught and bowled by Taijul Islam for 74, which came off 105 balls and included 11 boundaries and a six.
"Will has been in our Test squad as batting cover for the past two series and he should be confident following some strong performances domestically and for New Zealand A".
Williamson suffered a shoulder injury while fielding in Bangladesh's first innings in the second Test in Wellington, which New Zealand won by an innings and 12 runs.
Williamson took no further part in the day's play and went for a scan on the shoulder which proved inconclusive and he will have a second scan on Tuesday. When Taylor was out for 200, New Zealand was 421-5 and already 210 runs ahead.
"If things progress as we hope, then still going to the IPL shouldn't be a problem to him", said Stead. "It's very disappointing to loss the Test inside three days". But his share of the record lasted only minutes before Taylor reached his 31st half century. In doing so he overtook his mentor Martin Crowe, who scored 17 centuries in his celebrated career.
Talking about BJ Watling, who hurt his hamstring while warming up on the fifth morning, Stead said the wicketkeeper-batsman was being kept away from the action so that he can be fit for the third Test.
Trent Boult then removed dangerman Tamim Iqbal with the second ball of the Bangladesh second innings.
Liton Das (33) and Soumya Sarkar (20) chipped in with small contributions for the tourists, but they were unable to make the most of the platform set by Tamim and Shadman. Tamim hit the first ball for four; Boult smiled ruefully, then produced an nearly unplayable delivery which swung, then seamed back to bowl Iqbal.
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