The Hawks had to come back from a 13-point half-time deficit to record the victory as well, but they managed a blistering third quarter and that was enough to set up the 82-79 win.
Cairns started the game strongly opening up a seven-point quarter-time advantage after scoring an impressive 24 points and then adding another 22 in the second period to be in control of the contest leading 46-33 at the main break.
However, the Hawks then caught fire in the third period putting on 27 points and restricting the Taipans to just 10 to go from being 13 points down to four points up, and then holding on down the stretch to record the important road victory.
That means that Wollongong has beaten the Taipans in Cairns twice now this season with the Hawks improving to a 6-9 record on the season having won two straight matches, and four of their last six after beginning the season losing six of their first seven games.
Wollongong leapfrogged Cairns, New Zealand and Sydney with the win also to now sit in fourth position on the ladder with the 4-10 Townsville Crocodiles on the bottom.
Meanwhile, Cairns has now lost two straight matches after a run of winning four of five matches with the Taipans sitting in second last place at 6-10.
Wollongong import Kevin Tiggs top-scored with 20 points and four rebounds with his fellow import Rotnei Clarke adding 18 points and three assists.
Hawks captain Oscar Forman contributed 16 points and eight rebounds while point guard Rhys Martin finished with 11 points, four rebounds and three assists.
Taipans import Demetri McCamey led the way for his team with 18 points, five rebounds and five assists.
Stephen Weigh finished with 14 points as well and Clint Steindl scored 14 to go with five rebounds and three assists while hitting 4-of-7 from three-point range.
Centre Matt Burston added eight points, 10 rebounds and two assists but point guard Jamar Wilson struggled with just six points on 1-of-9 shooting from the floor.
Round 13 of the NBL continues with two matches on Sunday with the Adelaide 36ers hosting the Sydney Kings and the Townsville Crocodiles hosting the Perth Wildcats.