Ben Garuccio sealed the shootout after Sydney goalkeeper Harrison Devenish-Meares saved Xavier Bertoncello's effort, leaving most of a sold-out crowd at McDonald Jones Stadium devastated.
Patrick Kisnorbo's Sydney will bid for a record-extending sixth league title at Auckland FC, having been held 1-1 at home by the Jets in the first leg.
Newcastle won the Australian Cup in the off-season and the Premier's Plate for finishing top of the table at the end of the regular season.
But their bid to become the first team to complete Australian football's "triple crown" fell one trophy short.