Carey's 98 drags Australia home in New Zealand Test thriller
Carey and Mitchell Marsh have struggled for form but their formidable 140-run partnership rescued Australia at the Hagley Oval in Christchurch.
New Zealand's wait for a first home Test victory over their neighbours in more than three decades goes on.
"Something we spoke about today was keeping that scoreboard running, 200, 190, 180 (to get)," said Australia captain Pat Cummins, hailing Carey for his superb innings.
"As a fielding side you do notice that, you do start feeling the pressure build up.
"It's our strongest suit -- we're all really positive batters."
Carey and Marsh produced a vital partnership when the tourists had their backs to the wall at 80-5 in their chase of 279.
New Zealand captain Tim Southee said that partnership was the "big moment" in the Test.
The hosts losing the upper hand was the story of the series.
"We've been able to make early in-roads in every innings, which is pleasing, but I guess on the back of that you want to be able to nail it down," Southee said.
"But that's what you get when you play the top side in the world. They bat deep."
At 220-5, a nail-biting Test took another turn on Monday afternoon when Black Caps seamer Ben Sears claimed Marsh and Mitchell Starc in successive deliveries.
It left Australia needing a further 59 runs with three wickets remaining.
Skipper Cummins joined Carey to bring the tourists home.
"I kept to a really solid game plan and read the conditions and read the bowlers," Carey said.
"I guess losing one wicket this morning was okay. We got through to lunch and then that's when the game opened up a little bit and the partnership started to flow."
The series sweep earned Australia valuable points in the World Test Championship standings.
New Zealand were left deflated after starting the fourth day with high hopes of a first home Test victory over their rivals in 31 years.
On the attack
When Australia resumed the day at 77-4, after a one-hour delay because of rain, Marsh was dropped on 28 by Rachin Ravindra in the second over. Travis Head was out on the next ball from Southee.
New Zealand were buoyant, aware that Marsh and Carey were struggling for form, with Marsh coming off back-to-back ducks.
Carey had compiled just 27 from his three previous innings in the series.
The Australian pair found their touch when it mattered most.
Rather than be cautious, they went on the attack at more than five an over in the morning session as batting conditions became easier with the ageing ball.
The breakthrough New Zealand desperately sought came after lunch when debutant Sears took his double.
Marsh, who made 80 off 102 deliveries, went lbw and Starc followed first ball, caught at square leg by Will Young.
The hat-trick ball however was wide of the mark and the new batsman Cummins edged it for four.
Carey had an anxious moment when given out lbw to Matt Henry on 19 but on review the ball tracker placed the ball outside leg stump.
He gave few other chances in a 123-ball innings which included 15 boundaries.
For New Zealand, Sears took 4-90 while Henry's 2-94 gave him nine wickets for the Test.