Pakistan won the toss and batted at the Adelaide Oval but was all out for 213 in the 50th over, with paceman Josh Hazlewood taking 4-35 to justify his selection recall for Australia.
The Australians lost early wickets and withstood a torrid spell from Wahab Riaz (2-54) in the middle of the chase, before allrounder Watson hit the winning runs with a boundary to lift his score to 64 and Australia's to 216-4 in the 34th over.
Riaz was desperately unlucky to have two catches put down, especially Watson on 4. At that point, Australia was 83-3, Riaz was firing at 150 kph, and the allrounder was shaky.
Watson weathered Riaz and forged an 89-run fourth-wicket stand with Steve Smith (65), and an unbeaten 68-run stand with Glenn Maxwell (44 not out), who was also dropped early in his innings off Riaz.
"Extremely happy, a close game in the end — the way Shane Watson hung in there was fantastic," Australia captain Michael Clarke said. "That's pressure of the finals. You're under the pressure all the time, whether with the bat, in the field, or with the ball."
Clarke praised Riaz, who bowled with venom.
"You catch Watto at fine leg, it could have been a lot tighter," Clarke said. "Wahab bowled really well. Really tested us out."
It was a disappointing end for Pakistan veterans Misbah-ul-Haq and Shahid Afridi, who were set to retire from one-day cricket after the World Cup.
Misbah said batting let his team down again, as it did in the opening losses to India and West Indies before Pakistan rallied to win four straight pool matches to qualify for the knockout stage.
Riaz's bowling was the highlight of the game for the 1992 champions. Misbah vowed his attack, without the injured Mohammad Irfan, wouldn't be intimidated by the Australian batsmen, and would match aggression with aggression.
"He bowled his heart out, he's been a totally different bowler throughout this tournament, I've never seen spells like that," Misbah said of Riaz.
Left-armer Riaz delivered, removing David Warner (24) in the ninth over, and Clarke (8) in the 11th. He greeted Watson with perfectly directed short-pitch deliveries and glares.
After ducking and weaving for a couple of overs, Watson hooked Riaz to Rahat Ali, who put down a regulation chance at deep fine leg at 83-3. It was a genuine game-changer, with Watson and Smith combining to steer Australia back on course for the win.
Smith's assured 69-ball knock ended when he was adjudged lbw to Ehsan Adil at 148-4 in the 27th.
The reintroduction of Riaz to the attack should have yielded an immediate breakthrough but Maxwell's miscued, thick top edge was dropped by Sohail Khan running in from third man.
From then on, it was all Australia. Watson hit seven boundaries and a six in his 66-ball knock, his second half century since a recall after he was dropped against Afghanistan, and Maxwell clobbered five fours and two sixes in his 29-ball innings.
Hazlewood also extracted pace and bounce to prove his selection ahead of Pat Cummins was worthwhile.
Misbah's decision to bat backfired as Pakistan slumped to 24-2 in the sixth over, with Mitchell Starc removing in-form opener Sarfraz Ahmed (10) in the fifth over, and Hazlewood taking his first wicket in the next over to dismiss Ahmed Shehzad (4).
Misbah had a let-off before he'd scored when a delivery from Hazlewood brushed his thigh pad and grazed his leg stump, making the bail flash without dislodging it.
He shared a 73-run partnership with Haris Sohail (41) for the third wicket. But just as confidence was growing, Misbah attacked part-time spinner Maxwell (2-43) and was caught on the boundary.
Five of the Pakistan batsmen got decent starts but didn't go on, with Sohail leading the run-scorers with 41. While Pakistan heads home, four-time champion Australia will travel to Sydney for Thursday's semifinal against India.