The division's bottom team ended a run of 14 games without victory as it enhanced their chances of climbing off the foot of the table before the end of the campaign.
The Mariners sit third but their finals series hopes will go down to the last round of games, which sees them host Western United on Saturday, if Perth Glory beat Brisbane Roar on Wednesday.
Having dominated the opening exchanges at Central Coast Stadium, the hosts' evening took a turn for the worse in the 27th minute when they were hit by a well-executed counter-attack.
A poor headed clearance landed to 16-year-old Archie Goodwin, who made the most of the space he was afforded to play in Ray O'Donovan for an excellent finish into the far left corner.
Newcastle made it 2-0 just six minutes later, Lucas Mauragis twice winning the ball high up the pitch before latching onto Angus Thurgate's through pass to squeeze the ball home.
Central Coast thought it had found a way back into the game before the break, only for a Daniel Bouman close-range strike to be ruled out for offside.
Alen Stajcic's home side started the second period in similar fashion to the first, controlling possession and constantly probing the visitors' backline.
But they came up against a surprisingly obdurate Newcastle defence that, ultimately, did not give up a chance of real note as they eased to a deserved three points.