Carrusca's 28th minute strike secured a vital three points for the Reds in the race for the Premiers' Plate, despite a spirited performance from the Jets.
Newcastle was desperate to avoid the seven-goal humiliation it suffered last time the teams met.
Yet it was Adelaide that looked more comfortable early on and the Reds the ball in the back of the net on 13 minutes when Osama Malik poked in from close range after a goal-mouth scramble.
But it was ruled out for offside, with replays showing it was a close call.
Newcastle was looking dangerous on the break and after Edson Montano broke into the area and pulled the ball across goal, it fell invitingly for Mitch Cooper. His close-range shot was cleared off the line.
Adelaide's pressure told on 28 minutes. A ball over the top into the area was taken down by Cirio, who shot from a tight angle.
Ben Kennedy saved the initial effort, but Marcelo Carrusca was on hand hand to sweep the ball in and give the Reds a 1-0 lead.
While the Jets responded well to going down by creating a number of decent chances, the Reds almost added to their lead before the interval.
Cirio again was the architect as his cross found Bruce Djite right in front of goal. The striker's point-blank shot was expertly saved by Kennedy on the line.
Five minutes into the second half Newcastle had a glorious chance to equalise. Enver Alivodic played Ben Kantarovski through on goal. The midfielder steadied himself, but his delicate volley went just wide of the post.
A minute later Jacob Pepper drove the ball across goal, which Montano got on the end of. Unfortunately for the Jets his effort hit the post.
There was a few tense moments on 78 minutes when Nigel Boogard was treated for a suspected neck injury and had to be stretchered off with a neck brace. The club later reported the defender had full movement in his arms and legs.
Having used all their substitues the Reds had to finish the game with 10 men.
Adelaide managed to hold out for a precious three points that takes it to within two points of A-League leader Wellington Phoenix.
Reds coach Josep Gombau admits while the his side was only hoping to secure a top-four finish and a coveted home final, he now has his eye on the prize.
"It is good to get to the last four games and still have a chance to finish top," he said.
"But this feeling we have, the other four teams will also have the same.
"In the end we just have to go game by game... and if in the last game we still have a chance to get to the top - perfect. If not, we'll try to get a final at home, which I think is possible."
