The left-handed opener, who served a 12-month suspension for his part in the sandpaper scandal against South Africa in March 2018, hit 107 off 111 balls as his side finished 307 all out.
Mohammad Amir’s five for 30 and Imam-ul-Haq’s assured half-century threatened to derail the defending champions’ bid to bounce back from Sunday’s defeat to India.
But Pakistan eventually fell short as their chase ended on 266 all out with 26 balls remaining, partly due to Pat Cummins’ three for 33.
Australia captain Aaron Finch, who also impressed with a knock of 82, had backed Warner to return to his “dangerous best” in the build up to the match.
The 32-year-old justified his skipper’s faith in style, hitting 11 fours and a six and exuberantly punching the air to celebrate his ton.
Warner’s opening partnership of 146 with Finch was also the highest of the competition so far.
Their impressive alliance surpassed the 142-run stand between Bangladesh duo Shakib Al Hasan and Mushfiqur Rahim in the victory over South Africa.
Following a World Cup record three games rained off in five days, the International Cricket Council would have been relieved to see dry, albeit cold and cloudy, conditions in Somerset.
Pakistan were back in action for the first time since upsetting hosts England nine days ago after being frustrated by Friday’s washout against the West Indies.
They wore black armbands in respect of the recent deaths of former batsman Akhtar Sarfraz and Test umpire Riazuddin.
Amir began with a maiden after Pakistan won the toss and opted to bowl, before their momentum was stifled by the recalled Shaheen Afridi conceding 24 runs off two expensive overs with the new ball.
Finch, who bludgeoned six fours and four sixes during his hefty knock, benefited from slices of fortune as he survived a dropped catch from Asif Ali at slip, in addition to a strong lbw appeal which went to review.
He was eventually the first man out on the opening ball of the 23rd over after smashing Amir high and hard into the covers to leave Mohammad Hafeez with a straightforward catch.
Australia were still looking comfortable. However, after Warner was caught by Imam at deep point having sliced an Afridi delivery high into the air to leave the score 242 for four, the middle and lower order collapsed.
Spearheaded by the pace of Amir, Pakistan removed the final six wickets for just 30 runs in the space of only seven overs to give themselves a far more realistic target to chase.
Cummins ensured their response got off to a disheartening start as he removed Fakhar Zaman, caught by Kane Richardson at third man, for a duck at the start of the third over.
Babar Azam’s 30, Imam’s composed 53 and 46 from Hafeez steadied the ship slightly.
But the 1992 world champions lost a costly four wickets for 24 in 30 balls, beginning with opener Imam being caught down the leg side by wicketkeeper Alex Carey to become Cummins’ second victim.
Hasan Ali briefly entertained with 32 from only 15 balls before becoming Richardson’s second wicket.
Australia had to be patient but eventually wrapped up a third win from four.
Mitchell Starc removed Wahab Riaz (45) and Amir, for a duck, in the space of three balls in the 45th over, before Glenn Maxwell ran out captain Sarfaraz Ahmed (40) with a direct-hit.