Warner and skipper Finch opened the Australian innings with a 146-run stand after Pakistan won the toss and elected to bowl first.
David Warner posted his first international century since returning from a 12-month ban to launch Australia's innings but fell for 107 and Pakistan rallied to dismiss the defending champions for 307 at the Cricket World Cup at Taunton.
Left-arm paceman Mohammad Amir led the Pakistan attack with a career-best 5-30, and Australia's lower order crumbled to lose the last six wickets for 30 runs in seven overs.
Warner and skipper Aaron Finch (82) opened the Australian innings with a 146-run stand after Pakistan won the toss and elected to bowl first. The Australians, after reaching 165-1 halfway through their allotted overs, will be disappointed with being dismissed with an over to spare on Somerset's relatively small Country Ground.
Warner's 15th century in one-day international cricket and his first in any format for Australia since a test against England in December 2017 was the highlight of the innings for the five-time champions.
He wasn't exactly back to his best, but he still reached triple figures from 102 balls and stroked 11 boundaries and a six in the process.
He was only jeered by the heavily pro-Pakistan crowd when he was dropped cold by Asif Ali at third man on 104, but that was more likely frustration at yet another fielding error from the Pakistani team.
His innings came to end with Australia at 242-4 in the 38th over when he miscued Shaheen Afridi to Imam-ul-Haq at deep point.
From then on, it was mostly one-way traffic with Pakistan dominating at the end against an Australian batting order that was shuffled around to accommodate the absence of allrounder Marcus Stoinis.
Australia entered the game with an eight-game winning streak in ODIs against Pakistan, but Pakistan is coming off a morale-boosting win over top-ranked England.