The win was just the third of the season for the Reds and a positive response after a humiliating 5-0 home thrashing a week ago at the hands of Perth.
The bottom-placed Reds are still five points adrift of second-last Central Coast, who face Melbourne Victory on Sunday, while the Jets drop out of the six on goal difference.
The first half was devoid of any real clear-cut chances with both sides slugging it out and trading blows in the middle of the park.
Jordan O'Doherty had a shot from a tight angle saved by Jets goalkeeper Jack Duncan after eight minutes, while Andrew Hoole and Andrew Nabbout were looking dangerous for the visitors.
United had a massive scare on 26 minutes when star midfielder Isaias looked to have injured his knee, but continued on.
Morten Nordstand went close just after the half hour with a looping header which Reds keeper John Hall tipped around the post before crashing face first into the upright.
Nabbout had two efforts fly over the bar late in the first half before Adelaide defender Michael Marrone's long-range effort was deflected for a corner.
Isaias was unable to continue for the second half and was replaced at the break, handing a debut to Jae-Sung Kim.
The Reds started the second term at a frenetic pace with Sergio Cirio and Carrusca combining well while Ma Leilei tested Hall with a powerful low drive.
On 53 minutes, Tarek Elrich broke down the left-hand side and provided a neat cut back for Kim but his shot was deflected wide.
Hoole was next to try his luck for Newcastle but his shot was blocked by some desperate Reds defending.
United eventually broke the deadlock on the hour after another marauding run from Elrich ended with him being brought down in the area by a combination of Nigel Boogaard and Daniel Mullen, with the former adjudged to have made contact.
Carrusca stepped up and coolly converted from the spot sending Duncan the wrong way.
Both teams then upped the intensity and it reached a flash point when Riley McGree fouled Ma Leilei and Jets midfielder Wayne Brown remonstrated with the young Reds midfielder.
Both players were booked as the challenges continued to fly in from the two sides.
The Jets pushed for an equaliser and Hoole was again involved but his deflected cut back forced a quick, reflex save from Hall.
Adelaide United coach Guillermo Amor was happy with his side's display and their response after last week's heavy defeat.
"It was good," Amor said.
"We play well; the attitude and the performance of the players was good."
However, Newcastle coach Mark Jones was less than pleased with the build-up to the penalty which led to the match winner.
"I'm disappointed to have conceded a goal," Jones said.
"It was a soft goal and should've been met outside the box and it's dubious as to whether or not it was a penalty."