Chasing 276 for victory in the first of five matches for the Chappell-Hadlee Trophy, New Zealand made good progress with 75 for the opening wicket between Brendon McCullum (45) and Peter Ingram (40).
Australia clawed their way back with three quick scalps, and it was up to stand-in skipper Ross Taylor to steady the innings.
Together with James Franklin, the pair added 69 runs (of which Franklin only made 12) before the latter went, 101-runs still adrift of the target.
Again, the hosts fought back with some lusty shots by Neil Broom, but Shane Watson made the major breakthrough when he had Man-of-the-Match Taylor caught in the deep for 70 off only 71 balls.
Two runs later, Broom followed him back to the dressing-room, and this might have ended the Black Caps' hopes, but Styris - a late inclusion for Captain Daniel Vettori who suffered from a stiff neck - had other ideas.
With 69 runs still to go and only nine overs remaining, Styris and Daryl Tuffey steadily increased their scoring rate, and even though Tuffey and Tim Southee fell in the chase, Styris kept his head and - with four balls to go - hit the winning run off Bollinger over long-off for his only six.
Styris finished with 49 off only 34 deliveries, which included seven fours and the six.
Earlier, having elected to bat, Australia were restricted to 275 for eight.
All the Australian batsmen got starts but seemed to struggle with the pace of the wicket at times, and the hosts would be very pleased to have held them to below 300.
Shane Watson had a good start, hitting a 31-ball 45 before getting a Jacob Oram delivery high on the bat to be caught by Colin Ingram in the deep.
A good catch from Martin Guptill in the covers sent Ricky Ponting packing for 44, and Michael Hussey (59) was the only one to pass the 50-run mark before Shane Bond clipped his off-stump.
Some good work by James Franklin and Daryl Tuffey in the middle of the innings ensured a grip on the Australians' momentum. Tuffey was the pick of the attack with 3/58.
Of some concern for the Black Caps would be Oram, who twisted his left foot and knee as he fielded in at mid-wicket, went down in a heap and had to be assisted off the field.
The teams now move to Auckland for the second match on Saturday.
Teams: