The Jets pinched the lead through Lachie Rose in the 67th minute and held on at AAMI Park to claim their second win on the bounce and their fourth victory in five matches.
Sixth-placed City have won just one game in their past six, scored only seven goals in 11 games, and have also had to deal with racism allegations against youngster Medin Memeti.
On Sunday, Memeti started, two days after coach Aurelio Vidmar confirmed the 18-year-old wouldn't be stood down while Football Australia investigates allegations he racially abused Brisbane striker Justin Vidic.
Mark Milligan's Jets were busy from the opening whistle.
Just two minutes in, Jets dynamo Clayton Taylor forced a near-post save from Patrick Beach, who collected another Eli Adams attempt three minutes later.
In the 23rd minute, City's Samuel Souprayen hit the post with a header, then two minutes later Beach came to City's rescue, denying Rose at point-blank range.
It was another impressive performance from the talented young City goalkeeper, in front of Socceroos assistant Hayden Foxe and goalkeeping coach Frank Juric.
In the 41st minute, Jets goalkeeper James Delianov made a terrific save to deny Memeti before Andrew Nabbout tapped home - but was ruled marginally off-side.
After a lengthy VAR consultation, the offside call was upheld.
In the 48th minute, Mark Natta turned a dangerous Emin Durakovic cross to safety, preventing Nabbout, in his 200th game, from scoring a near-certain tap-in.
Newcastle took the lead when City centre-back German Ferreyra dawdled in possession and Rose nipped in, pinching the ball and scoring.
City kept pressing for an equaliser and Lawrence Wong turned a shot wide in the 77th minute.
The home side appealed for a handball penalty without reward in the 84th minute.
In the 88th minute, Jets defender Joel Bertolissio broke away and had a chance to seal victory, but smacked his shot off the crossbar.
City peppered Newcastle's goal in the dying minutes without reward and the Jets held on.
Newcastle next take on Western Sydney away on Saturday, after City host leaders Auckland at home on Friday.
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