Australia was 41-0 off just 3.1 overs on Sunday when rain began to fall heavily in Sydney, just 11 balls away from the five overs required to constitute a match.
Mitchell Starc (2-22) and Kane Richardson (2-16) had earlier taken two wickets for the Australians after the hosts had won the toss and sent Pakistan in to bat.
Starc removed opener Fakhar Zaman and hard-hitting allrounder Imad Wasim for golden ducks, while Richardson also struck early.
But Pakistan captain Babar Azam saved the tourists, helping them rebound from 10-2 to 107-5 before Australia's target was revised to 119 in 15 overs.
The teams play the second match of the three-game series on Tuesday in Canberra, followed by the final one in Perth on Friday.
They will also play two test matches, beginning Nov. 21 in Brisbane and a day-night test in Adelaide from Nov. 29.