The Cats were forced to sub out Stewart before quarter-time but recovered to erase a 21-point deficit in their 17.13 (115) to 13.7 (85) victory in front of 99,597 fans at the MCG on Friday night.
Chris Scott's side will meet the winners of Saturday's Collingwood-Brisbane clash in next week's grand final.
But Stewart will miss the decider under concussion protocols in what Scott described as "shattering" circumstances.
And there is concern over key defender Jack Henry, who played through pain with a left ankle injury sustained in the first quarter.
Dangerfield produced one of the all-time great finals performances for the Cats with 32 disposals, eight clearances and three goals.
The 35-year-old skipper, in his 359th game, put his team on his back after Stewart's early departure.
"He was born to play at this time of year and I hope it continues for a long, long time," Scott said.
"He wasn't the only one but when we were under pressure I just thought he was so influential."
Fellow stars Bailey Smith (36 touches, six clearances) and Jeremy Cameron (three goals) were also influential, as Zach Guthrie (10 intercepts) stood up in defence and Henry fought on bravely.
Geelong, who finished second on the ladder, will contest their fourth grand final in 15 seasons under Scott and could become the first club to win five premierships this century.
Hawthorn, playing their first prelim in a decade, were left ruing a missed opportunity after throwing away a strong start.
The Hawks kicked the first three goals and jumped out to a 22-1 lead as Geelong lost key pair Stewart and Henry - the latter temporarily - to injuries.
A Dangerfield goal from a free kick breathed life into the Cats before quarter-time but Mitch Lewis's three first-half majors and a brilliant Nick Watson snap kept the Hawks ahead.
Hawthorn forward Jack Gunston was denied a shot in the goal-square, called for holding an opponent, and Dangerfield's bullocking work helped drag Geelong back into the contest.
A classy Tyson Stengle finish followed by a series of behinds put Geelong in front by a point at the main break.
Stengle and Dangerfield added further goals early in the third term and the captain's influence grew as the Cats seized control with the first four majors of the second half.
The Hawks weren't done with, kicking the next three against the run of play, but again it was Dangerfield who teed up Jack Martin for Geelong's steadying goal.
They added 7.4 to 3.1 in the so-called premiership quarter, turning for home 28 points in front.
Dangerfield drove another dagger into Hawthorn with his third major as rain fell early in the final term as the Cats held their opponents at bay.
Stengle (three goals) kicked the sealer and Shaun Mannagh (two) was also dangerous.
Veteran forward Guntson kicked three majors for the Hawks, whose midfield was well beaten.
Geelong dominated clearances (50-33) and inside-50s (66-40), and Hawks pair Jai Newcombe (20 touches) and James Worpel (16) were among the key ball-winners outpointed by the Cats' strong engine room.
"We handled their pressure, we handled their moments really well, but sometimes they were just a bit too good," Hawthorn coach Sam Mitchell said.
"We just had no answers for a couple of things but it wasn't a mental skills thing. It was just being not quite good enough on the day.
"We're pretty raw in our journey - it's the first time most of us have been here - and we'll be better for it. But it takes a lot of work to get here."
