Under Josh Fraser, the Blues have famously fought back from a 1-8 start to the season that cost Michael Voss his job, to first make the wildcard round in 10th place, then reach the elimination final.
After fighting back from an early 21-point deficit, the Blues outgunned Melbourne, who finished seventh in the regular season, to claim a 10.14 (74) to 7.13 (55) victory in front of 91,733 fans at the MCG on Saturday night.
"It was another sign of the growth in this group where momentum's against you, you stay connected, trust our system," Fraser said.
"Collectively it felt like a really mature performance ... they're growing, our players.
"Our players are just growing in different scenarios and finding different ways to win. We're not a finished product."
The Blues next face the sixth-placed Cats - who they beat by four points early in Fraser's initial caretaker coach tenure - at the MCG on Friday.
Adelaide will host the Western Bulldogs in Saturday's elimination final.
A toothless Melbourne were left to rue poor kicking going inside 50 and bad finishing, kicking just three goals across the final three quarters and going goalless in the last.
Newly-crowned Rising Star Jagga Smith (29 disposals, nine clearances) kicked two last-quarter goals and stood tall alongside Sam Walsh (39 disposals, six clearances).
Skipper Patrick Cripps (22 disposals) fought through a left knee issue and close attention from Jack Steele (23 disposals).
Blues recruit Ben Ainsworth (three goals, 21 disposals) was everywhere, and Harry McKay jagged two goals.
Jacob Weitering was huge in defence with help from Harry Dean and Nick Haynes.
Melbourne skipper Max Gawn (27 hitouts, 31 disposals) started well but was reined in by Marc Pittonet.
Star midfielder Kysaiah Pickett had plenty of the ball but his finishing was left wanting, kicking three behinds, while the Demons clearly missed key forwards Jacob van Rooyen (suspension) and Matt Jefferson (knee).
"That probably sums up our night a little bit," coach Steven King said of Pickett's off night.
"It's a bit symbolic, really, of the game.
"A bit frustrating early. We had some momentum and weren't able to really punish them and put that ascendancy on the scoreboard.
"And even later - not just Kozzy, but there were a few opportunities for us. We just didn't take our chances, which you need to do in finals, obviously."
Jake Bowey (26 disposals), Steele and Harvey Langford (21 disposals) fought hard for Melbourne.
The Demons, without defender Jake Lever (toe) and forwards Jacob van Rooyen (suspension) and Matt Jefferson (knee), were hot early against a nervous Carlton and led by 21 points late in the opening term.
McKay steadied the Blues just before quarter-time, kicking off a run of five straight goals that ended with Brodie Kemp putting Carlton in front for the first time.
"At no stage did we look like we were fazed by not having the momentum," Fraser said.
Melbourne led by a point at halftime, then had 17 inside-50s to Carlton's nine in the third quarter, but were let down by poor kicking going forward.
Carlton snatched a four-point lead at the final change, then never looked like losing.
Melbourne, who kept butchering chances to fight back and still haven't won a final since their 2021 premiership - losing five at the MCG - farewelled retiring pair Tom McDonald and Jake Melksham.
