Earlier, Otago had slumped to three for 15 with Aaron Redmond spooning an ugly cross-bat shot straight back to the bowler Anton Devcich. Hamish Rutherford over committed and was run out at the non-striker's end, and Neil Broom charged Southee and got a healthy edge.
At the half way stage, Otago was 46 for four and in desperate need of a substantial partnership.
Ten Doeschate and Bracewell provided the relief. The pair added 66 for the fifth wicket.
Ten Doeschate probably took 15 or 20 deliveries before he started to really get going. He whacked five fours and two sixes in a fine innings.
Bracewell (31 off 20) chimed in with some crisp lofted drives and some chunky shots over midwicket as the pair brought up their 50-run partnership off just 32 balls.
They dragged Otago back into the match and some lusty blows from Butler (12 off 5) and James Fuller, who swatted two sixes off the last over to score 27 from 11 deliveries, help the visitors post a competitive total.