Newcastle started on the front foot, with Edson Montano immediately testing Jamie Young in the Brisbane goal, before up the other end, Steven Lustica saw his shot tipped onto the woodwork by Ben Kennedy.
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Brisbane were doing all of the running, but Kennedy was proving tough to beat in the Jets goal, making numerous saves during the opening half-hour.
Just before the interval, Lustica struck the woodwork for a second time as Brisbane pushed for an opener, but the visitors survived to remain on level terms at the break.
The Jets improved in the second half with Lee Ki-je being denied by Young, but with 19 minutes left, Brisbane went ahead thanks to substitute Kofi Danning, who got on the end of a cross from the flank to finally breach Kennedy's defences.
However, six minutes later, Newcastle were back on level terms through Montano, who controlled the ball neatly inside the penalty area before poking it into the net.
Newcastle looked like they were on course for just their 11th point on the road this season, but with four minutes remaining, Jackson reacted fastest to net the decisive goal from close range.