Goals from defender Kew Jaliens - returning to haunt club that spurned him - Frenchman Harry Novillo and substitutes David Williams and Iain Ramsay saw off the desperate Jets who remain anchored to the foot of the A-League table.
The win, witnessed by a disappointing crowd of just 5,867, saw City jump back into the top six - two points ahead of Brisbane which faces Sydney FC on Sunday - but having played three games more.
For the Jets, it was further confirmation that a total rebuild is needed in the off-season to lift the club's nosediving fortunes.
Novillo was full of adventure and intent early on and curled a 20-metre shot just wide in the sixth minute as the Jets back-peddled in the face of concerted City pressure.
He spurned an ever better opening in the 12th minute when he spooned his effort wastefully over the bar from inside the area after being set free by Aaron Mooy's perceptive pass.
But the breakthrough came in the 18th minute when, of all players, ex-Jets skipper Jaliens was left unmarked at a corner to sweep Mooy's delivery past keeper Ben Kennedy from close range.
There were muted celebrations from the Dutchman out of respect for his former teammates.
But, having been shown the door by the Jets for being a part of a group of players seeking to dethrone coach Phil Stubbins, the goal's significance would not have been lost on him.
Any hope the Jets had of getting something out of the match all but disappeared a minute after the break when Novillo took full advantage of some slapstick defending to plant the ball past Kennedy for his first goal for his new club.
City's misfiring marquee Robbie Koren should have made it three in the 56th minute but instead blazed his shot over the bar.
However, he atoned in the 63rd minute, picking out Williams with a pin-point pass which the striker raced onto to desptach past Kennedy to kill off the contest.
Ramsay inflicted further pain on the Jets in the 88th minute, latching onto Mooy's perfectly weighted pass to steer the ball past Kennedy for City's fourth.
"We still want to keep the pressure on (Brisbane) and know that we're still in it," City coach John van't Schip said.
"The reaction today was good and I think for the morale it was very important."
Stubbins called it a step backwards for his club.
"You can't hide behind a performance like that," Stubbins said. "From start to finish we weren't at the races. We were clearly outplayed by a better team."
