The win means Australia will finish Group C in third place but with the final games of Group D still to be played, their opponent in the Round of 16 is not yet known.
However, that game will be played either Tuesday night or early Wednesday morning AEST.
Australia recorded their most complete performance of the tour so far, shooting 58% from inside the arc while holding their opposition to 33% shooting overall.
Free-throws remain a concern as Australia again got to the charity stripe at will but struggled to capitalise on those opportunities, hitting just 23-34 (68%).
Tom Fullarton recorded another scintillating performance, setting the tone for his team with 19 points and eight rebounds while Matthew Johns was superb both inside and outside the paint, collecting 17 points.
Nine of those points came from beyond the arc with back-to-back makes in the third quarter breaking the match open.
Following two disappointing starts in their first two games, Australia began this contest with cooler heads and that composure converted to the scoreboard as they gained an early advantage.
Their offence showed signs of crumbling late in the term as Finland's pressure caused consecutive turnovers, allowing them to finish the first quarter on a 12-1 run.
The Aussies quickly regained their composure in the second period on the back of a three-point play from Matthew Johns though before Tom Fullarton put himself on the highlight reel with a gorgeous spin move lay-up in transition.
Australia won the second term 18-11 to take a half-time lead for the first time in the tournament and when Johns nailed two three-pointers in the third quarter, Australia had finally fully wrestled the momentum.
Aside from Fullarton and Johns, Callum Dalton impressed with seven points, seven rebounds and two blocks, Samson Froling had seven points, ten boards and four assists while Sean MacDonald added seven points and two assists.
The box score for the match can be found here while the full replay is available via FIBA below.