But a star turn from Cairns back-up big man Nnanna Egwu kept the home side in the fight.
The Chicago native thrived with extra minutes, scoring 10 points in the first half.
"The coach is always talking to me to be ready. There isn't any game where I'm not locked in whether I'm on the bench or the floor." Egwu said.
Sobey would hit back in the third and he was joined by Adelaide sharpshooter Anthony Drmic, who shot five from five from beyond the arc to steal the lead from the hosts.
But Cairns captain Cam Gliddon broke out of a form slump to renew the crowd's hopes late in the third.
Having scored just five points until that point, Gliddon suddenly came alight, hitting a three to finish the third and another two to start the fourth to finish with 16 points.
Egwu was quick to follow his captain's lead, blocking two shots and throwing down a dunk to suddenly put the Taipans up by seven with five to play.
Adelaide coach Joey Wright subbed out his entire starting five to finish the match, clearly not wanting to risk any of his guns as the Taipans ran out four-point winners.
"We wanted to test some guys that we know will get minutes come the playoffs and I thought our young guys played well under the pressure," Wright said.
The teams will play again on Saturday in Adelaide with Cairns needing to win again to guarantee a finals berth rather than rely on other results.
"This is what you play for, this is a privilege to have this pressure," Taipans coach Aaron Fearne said. "We are in with a chance."
