Adelaide threw all of their resources at the Taipans in the third term as star big man Daniel Johnson dominated across the court, backed up by import Jerome Randle.
The visitors drew within seven points on a handful of occasions before Cairns accelerated again.
Imports DJ Newbill (28 points), Scott Machado (21) and Oliver (24 and 15 rebounds) were consistent all night, while reserve guard Jarrod Kenny (11 points) lifted his side with three consecutive three-pointers to close out the third term to give his side a 14-point lead at the final change.
Adelaide struggled to put up a fight in the closing quarter as a packed Cairns stadium lifted the Taipans into the finals.
Adelaide star Johnson would be left to rue his team’s performance after producing one of his career-best games.
The power forward knocked down 38 points, shot at 55 per cent from the field and banked six from international waters.
Randle would also finish with a triple-double, collecting 21 points, 10 assists and nine rebounds, but did not have the influence coach Joey Wright was hoping for.
With five matches remaining, the 13-10 Taipans should almost certainly play finals. Their next match is against South East Melbourne on Australia Day.
Adelaide (11-12) can still feature in the NBL post-season but are competing with five clubs for one spot in the run home.