The Edmonton bookkeeper lost the first two legs of the best-of-five first set, but reeled off the next three legs to take the set, which was televised live in Britain.
Stoddart, ranked 29th in the world, recouped and won the second set 3-0 to tie the match.
The 41-year-old professional player took the third set 3-1 and blanked King 3-0 to advance to the second round.
Stoddart survived despite an off day and it was King who exited to a standing ovation after making history.
"It was awesome," King told The Canadian Press. "It was just electric.
"Everybody was going crazy. It was wonderful."
"This was my dream and I lived it," she added.
In other Canadian action Friday, Scott (The Full Mounty) Cummings was beaten 3-0 by Britain's (Big) Cliff Lazarenko.
Cummings, 30, is a Hamilton native who now makes his home in England.
King, 36, admitted to butterflies as she waited in the wings at the Circus Tavern.
As for Stoddart, he was just glad to get it all over, noting he was in a no-win position against a woman.
"If I had lost, God, that would have been it, wouldn't it?" said Stoddart, a Newcastle native whose hobbies include taking in Newcastle United soccer games at St. James' Park.
"I could never go to St. James' Park again if I got beat. No disrespect to Gayl.
"That was massively hard for me and obviously massively hard for Gayl. I think she's great.
"To get up on that stage and play the way she did, I think she's a winner as well. Even though I'm going through to the next round and Gayl doesn't, I think she's a winner."
While King won the first set, Stoddart said he didn't panic.
"I know it's five sets, I've been here before."
"I was glad to get a set," said King. "I didn't really actually hope for more than that, but it seemed like I lost my darts in the second set and I couldn't get them back."
But she acknowledged it was a landmark day for women.
"There's definitely women out there that who can do the job ... that can come in her and play those guys."
But Stoddart, while acknowledging the women's level was "very, very high," said he would rather see men and women have their own world championships.
King, ranked seventh in the women's world rankings, was listed as a 1,000-1 outsider to win the title.
The Canadian won 1,500 pounds ($3,370 Cdn) and more than a few fans.
The Professional Darts Corporation -- a spinoff circuit created when top players split from the British Darts Organization -- invited eight women to a playoff for one berth in the 32-person field at the world championship.
Seven turned it down, electing to go to the rival organization's tournament.
King is no stranger to playing men back home in league action.
But Friday's game was her first professional game against a man.
Originally from Newfoundland, King took up competitive darts in 1988.
She had competed internationally before and holds the Canadian women's singles, doubles and mixed doubles crowns.
She is slated to return to Edmonton on Jan. 5.
