Had Australia not spilled four catches the day would have been even grimmer for New Zealand.
Opener Martin Guptill was dropped at short leg on seven; Brownlie was spilled twice on three in the space of three balls and captain Ross Taylor was grassed on four.
This was not a case of a piercing Australian attack undoing New Zealand's best endeavours.
The Australian seam trio, including debutants James Pattinson and Mitchell Starc, were all over the show early on, unable to control the swing as opener Brendon McCullum got stuck into the new ball.
He took three fours in the opening over of the test, from Pattinson, and while much of Australia's bowling in the period was distinctly ordinary, New Zealand's batsmen found a range of ways to get themselves out.
Guptill softly tried to drive seamer Peter Siddle and edged a catch behind; McCullum rashly cut a short ball straight to point; Kane Williamson gently nudged a catch to short leg off offspinner Nathan Lyon, Taylor managed to drive a widish ball onto his stumps; and Jesse Ryder, in the over after the resumption, lashed a short ball straight to point.
It was wretched batting and while the Australian bowlers all had their moments, they lacked the consistent, penetrative edge the scoreboard might suggest.
Vettori worked the ball into the gaps around the ground and looked comfortable most of the time. Brownlie was skittish and could easily have been out three times before reaching double figures, but the key was he survived alongside Vettori.
Australia's three debutants were all in the action in the morning.
Starc got his first two wickets in test cricket; Pattinson benefitted from Taylor's loose stroke; while David Warner grabbed two catches.
At a disconcertingly early stage of the test, New Zealand have left themselves an uphill task to get back into the contest.
Scoreboard at stumps on day one of the first cricket test between Australia and New Zealand at The Gabba in Brisbane:
New Zealand
First innings
B McCullum c Warner b Starc 34
M Guptill c Haddin b Siddle 13
K Williamson c Khawaja b Lyon 19
R Taylor b Pattinson 14
J Ryder c Warner b Starc 6
D Brownlie not out 32
D Vettori not out 45
Extras (9b, 3wd, 1nb) 13
Total (for 5 wkts, 51 overs) 176
Fall: 44 (Guptill), 56 (McCullum), 78 (Williamson), 93 (Taylor), 96 (Ryder).
Bowing: J Pattinson 11-1-50-1 (2w, 1nb), P Siddle 15-5-29-1 (1w), M Starc 13-0-52-2, N Lyon 10-0-31-1, M Hussey 2-0-5-0.APNZ ks lb