Mark Milligan's Jets, who lost to second-placed Auckland last week, drew first blood when Kota Mizunuma lashed home a thumping strike from outside the box in the 32nd minute of the clash at Allianz Stadium.
Sydney could not be contained and hit back when Pedro Quispe slipped through young gun Tiago Quintal in the 68th minute, with the talented teenager taking a touch and rifling home.
The Sky Blues then had a penalty chalked off for offside, before Newcastle's Xavier Bertoncello broke away and teed up Gibson for the winner in the 94th minute.
"It was massive," Jets skipper Max Burgess, who was a clear man-of-the-match with a standout performance in midfield, told Paramount Plus.
"They threw so much at us in the second half - we had to suffer a lot.
"I thought we were still brave with the ball in hard moments and I'm just so proud of the boys who came off the bench and won us the match in the end."
The result means Australia Cup winners Newcastle (43 points) are four points clear of Auckland (39) and with a massive buffer on third-placed Melbourne Victory (35) and fourth-placed Adelaide (35), meaning an ACL Elite spot is almost locked in.
Sunday's result also doesn't particularly help Sydney, who are winless in three and sit fifth on 33 points with four games to go - amid coach Ufuk Talay being heavily linked to the top job at fierce rivals Western Sydney next season.
Sydney skipper Rhyan Grant, in his 400th appearance, thought he had equalised in the 97th minute but was caught in Newcastle's offside trap and left to taste defeat.
"It's been a pretty big week in terms of that milestone ... obviously with the football it's pretty disappointing," Grant told Paramount Plus.
"It was very disappointing in terms of results and where we're sitting at the moment in terms of the season
"But there's still a few games to go so hopefully we can turn it around and get a roll on."
The Jets have a tight turnaround to face Macarthur away on Thursday night, when Sydney are on the road against Brisbane.
