WA trailed for much of the game thanks to a combination of poor kicking for goal and some impressive play from its underdog opponent, but stepped up in the final quarter to run out 11.14 (80) to 9.12 (66) winners.
Behind by eight points at the final change after booting a wasteful 5.13 in the first three quarters, WA found range in the final term, piling on six goals to NT's two.
Coniglio, a tough and skilful midfielder tipped to be selected by Greater Western Sydney with one of its top picks in this year's NAB AFL Draft, booted two final quarter goals to put an exclamation mark on a fine individual display.
His on-ball partner O'Meara was equally impressive in the clinches.
Small forward/midfielder Shannon Taylor stepped up when the game needed to be won, kicking the first goal of the final quarter and proving instrumental in WA's strong finish.
Taylor and O'Meara are in the age bracket (those players who turn 17 between 1 January and 30 April) eligibile to be used as trade incentives for GWS, where the Giants can allocate up to four selections over the next two years to other AFL clubs for players with experience and/or draft selections.
Earlier, NT showed real character to bounce back from a scoreless opening quarter and play some outstanding free-flowing football through the middle part of the match.
Solidly built Tiwi Islands small forward Anthony Tipungwuti booted three goals for the home team and looked a constant threat, and Louis Egger impressed with his line-breaking run and ferocious attack on the ball.
After turning a 17-point quarter-time deficit into a three-point half-time lead it looked as though NT may cause a boilover, but the classy West Australians eventually ran over the top.
Northern Territory 0.0 4.5 7.9 9.12 (66)
Western Australia 2.5 3.8 5.13 11.14 (80)
GOALS
Northern Territory: Tipungwuti 3, Turner 2, Stafford 2, Collinson, Stokes Western Australia: Williams 2, Coniglio 2, Peters 2, Hamling 2, Eardley, Taylor, O'Meara
BEST
Northern Territory: Egger, Tipungwuti, Collinson, Turner, R Smith, Wilson
Western Australia: O'Meara, Coniglio, Hamling, Newman, Taylor
Match played at TIO Stadium, Darwin.