United, who parted ways with coach Chris Anstey after their loss in round one, lost for a second time before finally winning.
Darryl McDonald's time as interim coach started badly as United were beaten 88-73 by the Cairns Taipans.
Cameron Tragardh shot 18 points and had six rebounds at the Cairns Convention Centre.
But United finally got their win on Sunday, easing past the New Zealand Breakers 95-74.
American Jordan McRae hit a game-high 31 points to go with nine rebounds.
Corey Webster's 23 points had led the Breakers to a 101-80 win over the Adelaide 36ers on Friday.
Defending champions the Perth Wildcats recorded their first win of the campaign on Friday, easing past the Wollongong Hawks 69-59.
DeAndre Daniels double-double of 16 points and 13 rebounds led the Wildcats to their win.
Elsewhere, the Townsville Crocodiles edged the Sydney Kings 86-81 and the Taipans defeated rock-bottom Wollongong 91-89 in dramatic fashion to make it four wins from four.