The Tigers never trailed in the second of their four games scheduled in Australia. Alverson opened the contest with a three-pointer and would finish the contest with five treys.
"I am happy for the win," new Auburn head coach Terri Williams-Flournoy said. "It is exciting for the staff and the team to see some of the things we have been working on materialize.
"Everyone contributed in this win and that is good to see, especially when you are working with as few players as we are. We just have to keep working because we are not there yet. This was a good first step, but we have a long way to go."
Freshman guard Chadarryl Clay scored 20 points for the Tigers while sophomore guard Hasina Muhammad contributed 16 points.
Freshman center Nicole Tanner scored eight points and junior center Peyton Davis added seven. Senior center P.J. West scored four points while freshman forward Cabriana Capers was the team's other scorer with three.
Auburn led 26-18 at the end of the first quarter and was up 47-38 at halftime. The lead stretched to 64-54 at the end of three quarters.
The Dolphins made a fourth period run to cut the lead to 69-66 before Auburn pulled away for the victory as Muhammad and Clay scored eight of Auburn's final 12 points.
Cayla Francis led Cairns with a game-high 27 points while Jade Kennedy added 13.
Next on the schedule for the Tigers is a 10 p.m. CDT Saturday game vs. the Sydney Flames.