The South African-born wicket-keeper compiled a career-best 103 as the Black Caps recovered from 282-7 to post 469 all out by tea at the Zahur Ahmed Chowdhury stadium.
Last man Trent Boult also hit a personal best of 52 not out, helping Watling add a valuable 127 runs for the 10th-wicket on the newly-laid pitch that provided only slow turn to the spinners.
Bangladesh will begin their reply after tea, needing to match the rivals' huge total if they are to avoid defeat in the first game of the two-match series.
His valiant effort ended just at the stroke of tea when he was stumped off Mominul Haque, the eighth bowler deployed by Bangladesh during the innings.
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Watling hit six boundaries and two sixes as he surpassed his previous best of 102 not out against Zimbabwe in Napier in January last year.
Boult breezed past his personal best of 33 with a six off Shakib Al Hasan and returned unbeaten as Watling was dismissed attempting to pick up the scoring rate.
Martin was caught behind from a thin edge off Rubel and Anderson edged Razzak to first slip, giving the left-arm spinner his third wicket in the innings.
But Watling and Doug Bracewell prolonged the innings by adding 57 for the eight wicket.
Bracewell gifted his wicket when he attempted a rash sweep off Sohag Gazi, missed the line and was bowled for 29.