Skipper Kosta Grozos scored from the penalty spot in the 99th minute after Mitch Langerak clipped Lachie Rose over the head with his right arm as he came off his line attempting to clear the ball.
The contact, in the 80th minute, was initially waved away but after a VAR review, a penalty was awarded two minutes later.
The penalty was delayed by more than 17 minutes due to a medical emergency in the crowd, but Grozos kept his nerve to score.
Clayton Taylor latched onto a wonderful ball from Charles M'Mombwa and finished with aplomb to make it 2-0 in the 104th minute.
Rose tapped home a lovely cross from Kota Mizunuma in the 110th minute to seal Newcastle's first home win of the season at McDonald Jones Stadium.
After two wins on the bounce, Victory's woes from earlier in the season resurfaced - with Arthur Diles' charges dominating early chances but paying the price of failing to put them away.
Victory (25 points) sit fourth behind Western United on goal difference, six points behind second-placed Adelaide United and eight back from leaders Auckland FC,while the Jets (15) are nine points out of the top six.
Newcastle goalkeeper Noah James, playing his first ALM game since one appearance in August 2020, was the difference in the first half, making five saves.
James denied Victory dynamo Zinedine Machach in the 12th minute and Adama Traore in the 23rd.
Machach forced another excellent save two minutes later and Nishan Velupillay blasted over the bar in the 29th minute.
Newcastle scored in the 33rd but Thomas Aquilina was offside, before James denied Brazilian attacker Santos in the 39th minute.
Jets defender Phillip Cancar limped off in the 42nd minute but Newcastle came out of the break with added impetus and Taylor dragged a strike just wide of the far post almost immediately.
Rose thought he had opened the scoring in the 54th minute, but Eli Adams was just offside in the build-up.
But the Jets never stopped pressing and ran out the game, that ultimately lasted almost 115 minutes, in style.
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