The 20-year-old from Montreal harried and chased third seed Halep from the baseline, producing a series of forehand winners.
The match was interrupted three times. After four games Halep, 22, needed treatment on a sore ankle. Then in the tiebreak a spectator was taken ill in the sunshine and had to be led from the stand.
On Bouchard's first match point Halep served an ace, but 13th seed Bouchard complained she had been distracted by a noise in the crowd. She argued with the umpire Kader Nouni but the point stood.
With Bouchard rattled, Halep saved four more match points but her intensity was shot and she sent a ball long to offer the Canadian her sixth chance.
Bouchard thumped down a big serve that the French Open finalist could only push into the net.
"It was a little crazy. I have never ended a match like that," Bouchard said. "I'm happy I kept my focus and didn't get distracted and played well in the last game."
The Canadian, who reached the semi-finals at both the Australian and French Opens this year, meets 2011 champion Petra Kvitova in Saturday's final. The Czech beat compatriot Lucie Safarova in the first semi-final.
"I'm really excited ... it's my first grand slam final so I'm just going to go for it. I will probably have my toughest match yet so I'm looking forward to the challenge," a beaming Bouchard said.
"My coach will watch her play and give me some tips on how she plays, but I'm just going to go out there and play my game. I think I can play even better than I did today."
The semi-final victory shot Bouchard into the world's top 10 in only her second year on the professional tour.
(Editing by David Goodman)
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