Stoinis hammered six sixes and two fours during a swashbuckling performance that pushed Australia to 164-5 off 20 overs after they had slumped to 50-3 earlier in the innings.
David Warner helped provide some stability with a half century as Australia eventually got going after captain Mitchell Marsh and Glenn Maxwell fell off successive balls to seamer Mehran Khan in the 11th over.
After a steady couple of overs, Stoinis went on the attack, dominating a 102-run fourth-wicket partnership which effectively wrested the initiative away from the Omanis.
Warner, in his final tournament before international retirement, compiled 56 off 51 balls (six fours, one six) before falling in the penultimate over.
Four of Stoinis’ six sixes came in the 15th over of the innings, bowled by Mehran, and triggered such a pace of acceleration that the 2021 champions were able to more than double their total over the last six overs of the innings.
Beaten in a super over in their opening encounter by Namibia at the same venue three days earlier, the Omanis seemed in the mood for the fight with the early dismissal of Travis Head followed by the Marsh-Maxwell double-blow.
However Australia’s competitive know-how saw them through that tricky period at the start of their campaign to become the first nation to hold all three global cricket titles – Test, One-Day and T20 – simultaneously.