Bruce was unbeaten on 42 off 41 balls and opener Sean Solia defiant on 62 when stumps were called at Allan Border Field on Tuesday.
The visitors were all out for 147 on day one but had moved to 2-191 in a second-day rally that began with Scott Kuggeleijn's five-wicket haul.
The Kiwi quick had the hosts fishing and some good catching meant Australia A went from 3-141 overnight to 263 all out.
Caleb Jewell (78) couldn't kick on to a big score while Queenslanders Jimmy Peirson (30) and Mark Steketee (32) and Mitchell Swepson (21 off 19) all chipped in.
South Australian Jordan Buckingham had Henry Cooper caught behind with his first ball to end New Zealand's promising 40-run opening stand.
He then picked up Nick Kelly, caught in the deep for 43.
But the Kiwis were untroubled after that, left-arm opener Joel Paris the only one of five bowlers used to go for less than four an over.
The unofficial Test is one of two between the two teams in Queensland, before three 50-over games.