The Jets were leading 2-1 in the 21st minute of Thursday's A-League Men match when defender Max Cooper was handed a red card for his second bookable offence.
It was a mere fight for survival from that point on for Newcastle and they were dealt another blow in stoppage time when midfielder Christian Bracco limped off with a knee injury, leaving the visitors with just nine men.
In a last-ditch bid to snatch a draw, Auckland threw their goalkeeper forward for the last two corners of the match, but the tactic backfired as the Jets unleashed a fast break that resulted in a 96th-minute sealer to Rose.
"I'm so lost for words. Going down a man early, we never gave up," Jets captain Kosta Grozos told Paramount.
"We always fought to the last minute, and to get that goal at the end was the cherry on top."
The result lifted Newcastle (15 points) into the top six, while Auckland (20 points) remain top.
In a chaotic start to the match, there were three goals, a red card and a serious-looking knee injury all inside the first 21 minutes.
Alex Badolato's day was over in just the third minute when the 20-year-old Jets striker, who has scored four goals this season, injured his right knee after stretching for the ball and twisting over it at an awkward angle.
The Jets opened the scoring in the seventh minute when Rose volleyed in a rocket cross from Clayton Taylor.
Auckland forward Jesse Randall equalised six minutes later with a curling free kick that beat Jets goalkeeper James Delianov at the near post.
Will Dobson put Newcastle ahead again in the 16th minute via an easy tap-in after Taylor's initial shot was saved.
But there was still more drama to come, with a poor first touch from Cooper leading to him clipping an opponent and receiving a second yellow card.
Auckland peppered Newcastle's goals for the remainder of the half, and could have easily entered the break with four goals to their name if they had been able to produce better finishes.
It was more of the same in the second half, with only desperate goalkeeping, clearances off the line and blocks saving the Jets, until Rose popped up for the late sealer.
Auckland fired in 23 shots to six for the match, but the Jets were clinical in attack and whole-hearted in defence.
The Jets have now posted three wins in NZ this season - two over Auckland, and one over Wellington.Â
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