Bad light stopped play midway through the second session before a huge rainstorm swept down across the city, leaving the home batsmen kicking their heels for the remainder of the day still 197 runs behind Pakistan's first innings score of 313.
Marnus Labuschagne, who was 23 not out, and Steve Smith, unbeaten on six, will resume on day three on Friday when no rain is forecast.
"I think we're starting to get used to it here in Sydney each year but yeah, it's frustrating to lose a bit of time to light and then now a bit of rain settling in," Australia captain Pat Cummins said.
The last three New Year's tests at Sydney Cricket Ground have been impacted by the weather and all ended in draws.
Australia hold an unassailable lead in the three-match series against Pakistan after victories in the tests in Perth and Melbourne but will be desperate to send Warner into retirement a winner on his home ground.
The 37-year-old had come through a single over with six runs to his name at the end of play on Wednesday and resumed with childhood friend Usman Khawaja under cloudy skies on Thursday.
He should have departed for 20 when Pakistan debutant Saim Ayub dropped a sitter in the slips, and was fortunate on 27 that his edge went between the slips and gully and ran to the boundary for four.
A bowling change for Pakistan did the trick with off-spinner Agha Salman coming on to remove Warner with his third ball, the Australian bamboozled by the spin and bounce and edging the delivery to Babar Azam in the cordon.
The crowd was initially silent but quickly roused into yet another ovation for Warner, whose runs took his career tally to 8,729 in 112 tests at an average of 44.53.
"It was pretty good ball he got there," Cummins added.
"He always finds a way to get himself up and he looked like a man on a mission when he walked out to bat. I'm sure he'll get a second innings out there to score a few more runs."
Khawaja followed for 47 before the weather disruption, ruled to have been caught behind after a DRS appeal off the bowling of Aamir Jamal, Pakistan's find of the series.
"Really happy with where it stands," said Cummins. "It's a really good wicket, it feels like there's plenty runs to be scored.
"So if we can get a first innings lead that would be good. A decent lead would be better and hopefully it'll start spinning."
