New Zealand batters struggled against Bangladesh's spin-heavy attack on a turning track in Sylhet but Williamson batted close to five hours for his cultured 104, which included 11 fours.
His 29th test hundred drew him level with Australia great Don Bradman and India stalwart Virat Kohli.
Captain Tim Southee (one) and Kyle Jamieson (seven) will resume New Zealand's bid to erase the 44-run deficit when play continues on Thursday in what promises to be a low-scoring contest.
Earlier, Bangladesh were all out for 310 after Southee claimed the last wicket of Shoriful Islam with the first delivery of the day.
New Zealand lost Tom Latham, Devon Conway and Henry Nicholls before reaching the 100 mark but Williamson featured in three half-century partnerships to keep New Zealand in the contest.
Daryl Mitchell (41) and Glenn Phillips (42) made useful contributions while Williamson held up one end.
The top-order batter took a single off Nayeem Hasan to bring up his hundred before left-arm spinner Taijul Islam (4-89) breached his stubborn defence after Williamson attempted a forward defensive shot.
At 253-5, New Zealand looked set to grab the lead but Bangladesh claimed four wickets in the final session to leave the match evenly poised.
