In a blistering start, City were 3-0 up inside the first 25 minutes as Aaron Mooy from the penalty spot, Koren and Damien Duff all capitalised on some poor Jets defending to all-but ensure the result before half-time.
Koren then completed his treble after the break – either side of Edson Montano's header for the home side – before a late consolation for Jeronimo Neumann.
The big win was not only the perfect birthday present for coach John van't Schip – who turned 51 on Tuesday – but will also have the leading clubs looking over their shoulders at fast-improving City.
Meanwhile, Brisbane Roar and Sydney played out a tame 0-0 draw at Suncorp Stadium.
The contest was even in the first half with both teams creating a couple of gilt-edged chances.
Roar's Jean Carlos Solorzano and Sydney's Alex Brosque went the closest to finding the back of the net for their respective teams, but could not convert when well placed.
Brisbane were able to gain more possession in the second half but were unable to find a match winner, with a draw a fair result but not what either team needed.
