Kew Jailens and Adam Taggart netted either side of the break for the Jets, and although Fabio Ferreira reduced the deficit with 19 minutes remaining, the visitors held on to overtake their hosts in the A-League table.
Despite a lively opening, the scoreline remained goalless until 41 minutes, when Jailens converted a Nathan Burns corner.
Taggart doubled Newcastle's advantage seven minutes after the break with a chip over the goalkeeper, and that looked to have deflated Adelaide.
However, former Chelsea reserve Ferreira headed in from close range as the home side threatened a comeback, but they couldn't find an equaliser.
Nigel Boogaard was also dismissed in added-on time for United.