While City dominated the majority of the contest, the Jets made their more fancied opponents work for their eighth win on the bounce.
But in the shadows of half-time, Goad's 44th minute stike from outside the box left Newcastle goalkeeper Hannah Southwell little chance of keeping it out and broke the deadlock.
While the Jets tried to match City in the second-half, particularly defensively, their efforts in the final third lacked quality at times.
The win takes City out to an eight point lead at the top of the W-League ladder, while the Jets remain in fourth spot after Perth Glory went down 4-2 to Sydney FC in the final game of round 9 on Sunday night.
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