Opting to bat, the hosts put up a commanding 328/7 in 50 overs before bowling out India for 233 in 46.5 overs.
The daunting target notwithstanding, India started well with openers Rohit Sharma (34) and Shikhar Dhawan (45), with the latter playing the aggressor's role.
The left-hander was dropped by wicketkeeper Brad Haddin while batting at five but recovered to notch six boundaries and a six in his 41-ball innings.
Just when India were looking like they may give the hosts a scare, from 76/0 in the 13th over, India lost four quick wickets to be tottering at 108/4. Virat Kohli (1) and Suresh Raina (7) failed to provide the impetus and the loss of their wickets completely put India on the backfoot.
Ajinkya Rahane (44) and captain Mahendra Singh Dhoni (65) then tried to steady the floundering ship with a 70-run fifth-wicket partnership but the asking rate kept mounting.
After Rahane got out, the pressure got on to Dhoni, who despite scoring a run-a-ball 65, couldn't keep the team in contention.
The Australian pacers exerted their supremacy by scalping the last four wickets for just two runs.
The tournament's highest wicket-taker Mitchell Starc starred for Australia, picking 2-28 in 8.5 overs. Fellow left-arm pacers Mitchell Johnson (2-50) and James Faulkner (3-59) also chipped in.
Earlier, Smith and Finch's second-wicket partnership powered them to the first 300-plus total in a Cup semi-final with Smith scoring his fourth One-Day International (ODI) century.
India started well with pacer Umesh Yadav (4-72) taking big-hitter David Warner's wicket in the fourth over. Thereon, Smith and Finch took control of the proceedings.
Opener Finch was slow but managed to stick it out in the middle to score seven boundaries and a six in his 116-ball knock. He provided good support to Smith, who smashed his way to 11 fours and two sixes in his 93-ball innings.
India pulled things back as Yadav, Mohit Sharma (2-75) and off-spinner Ravichandran Ashwin (1-42) took four quick wickets.
Brilliant cameos at the end from Faulkner (21) and Johnson (27 not out) helped Australia hammer 89 runs off the last 10 overs to swell Australia's total.
Indian bowlers, who were impressive throughout the tournament, were taken for runs at the death.
Eventually, the target proved too much for India that ended the team's 11-match winning streak in the World Cup.
Losing captain Dhoni said opener Dhawan's dismissal was the turning point of the match.
"We got off to a very good start. Shikhar's dismissal was slightly on the softer side, at a time when we could have had the bowling under pressure. He didn't really need to play a big shot," Dhoni said.
"But you get pressure chasing 300 plus, makes you do things you don't want to do."
Dhoni also expressed his concern about the lower batting order failing to cope with the conditions and the Australian quicks.
"I don't think they (lower order) can contribute as much in these conditions. So, it makes it further difficult (to chase a huge score)," he said.
"But overall, I think it's a good exposure for them. Maybe next time when you are playing in other conditions, they'll know how to bat in these conditions and they'll do much better."
Australia skipper Michael Clarke said he was proud the way his team played.
"Obviously, I am really excited, the boys played some outstanding cricket," Clarke said.
"It's a wonderful achievement. We're proud to make the final but it's going to be tough against New Zealand."
Clarke heaped praise on Man-of-the-Match Smith for his defining knock.
"Smithy was hitting the ball so sweetly. He played an outstanding knock," he said.
It will be Australia's seventh appearance in the final where they will face co-hosts New Zealand -- in their maiden final appearance -- on Sunday at the Melbourne Cricket Ground (MCG).