Watling, the South African-born wicket-keeper, was unbeaten on 58 and last man Trent Boult was on six after the extended morning session at the Zahur Ahmed Chowdhury stadium.
The Black Caps, who resumed on 280-5, lost Bruce Martin and debutant Corey Anderson in the first two overs of the day to slip to 282-7.
Martin was caught behind from a thin edge off seamer Rubel Hossain and Anderson edged Abdur Razzak to first slip, giving the left-arm spinner his third wicket in the innings.
Bracewell gifted his wicket when he attempted a rash sweep off Sohag Gazi, missed the line and was bowled for 29.
He had hit a six and three boundaries in his 72-ball knock.
Watling, reprieved after being caught off a Rubel no-ball when on four, settled down to strike five boundaries in his fifth Test half-century.
Boult helped Watling add 36 valuable runs for the last wicket, keeping the hosts at bay even though the session was extended by 30 minutes following the fall of the ninth wicket.
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