New Zealand saw little ball during the opening exchanges and trailed 3-0 when Australian halfback Harry Nucifora landed a penalty goal.
But from the moment Jacobson charged over the line powerfully off the back of the scrum, it was apparent New Zealand were playing the game at a pace that was going to stretch Australia.
They scored in close (Isaia Walker-Leawere) or out wide (Tua and Will Jordan, the latter slicing through some porous defence).
They also enjoyed some luck when flanker Tom Christie was awarded a try, controversially, as New Zealand appeared to knock the ball on.
The game lost its shape in the final quarter, but New Zealand scored 186 points over three games, so will just need some fine-tuning and ensure the set-piece is humming in three weeks.
The 28-man squad for Georgia is due to be announced next week.
Samoa beat Fiji 39-29 to secure third place in the quadrangular tournament.
New Zealand 43 (Luke Jacobson 2, Isaia Walker-Leawere, Will Jordan, Tamati Tua, Tom Christie tries; Tiaan Falcon 5 con, pen) Australia 6 (Harry Nucifora 2 pen) HT: 29-6