New Zealand snapped a five-game losing streak and extended Cairns' woes in the process with an 89-78 NBL win.
Breakers coach Kevin Braswell was thrilled to grab the victory at the Cairns Convention Centre to keep in touch with the competition's top-four.
"This season will come down to the last three weeks I can guarantee you," he said.
"You can lose a couple of games and people will say you're out of finals contention or you can win a couple of games and people think you're definitely making the top four.
"But this season is really close. Cairns might have only won one game but they are a good side."
Former Taipans player Jarrad Weeks led New Zealand's scoring with 17 points.
The contest between the NBL's two bottom-placed sides didn't reach any great heights, but the Breakers outscored the Taipans 27-13 in the final stanza to snare the win.
The trans-Tasman visitors trailed 20-19 at the first break, but found an extra gear in the second term to lead by six at halftime.
That margin was blown out to 11 early in the third term before Cairns went on a huge scoring run to hold a three-point lead over the Breakers at the final change.
But the home side's hopes of a drought-breaking win were quickly dashed as the Breakers took control in the last quarter.
New Zealand had a range of scorers, with American import Shawn Long (16), skipper Tom Abercrombie (14), Shea Ili (14) and Tai Wesley (11) all registering double digits.
Long had 13 rebounds, while Wesley finished with five assists.
While still second last the Breakers (5-8) move to within two wins of fourth placed Brisbane, the New Zealanders also having a game in hand.
Melo Trimble led Cairns' scoring with 23, including two from the perimeter, while Devon Hall (14) and Nate Jawai (11) also contributed.
Taipans coach Mike Kelly was happier with the effort of his charges but rued lapses in the game which proved costly.
"Losing breeds frustration and that's where we are at somewhat because everyone wants to win," he said.
"We'll continue to be upset when we don't do well enough and we don't win games, but we know what we need to do - we need to do everything better."