Bouchard, from Westmount, Que., converted her sixth match point to complete the victory in one hour 34 minutes.
The 13th-seeded Canadian will next face sixth-seeded Petra Kvitova on Saturday. Kvitova beat fellow Czech left-hander Lucie Safarova 7-6 (6), 6-1 in the early semifinal.
"It's my first Grand Slam final so I'm just going to go for it," Bouchard told ESPN. "I'll have probably my toughest match yet so I'm looking forward to the challenge."
Another Canadian is in the final four of the men's draw. Milos Raonic of Thornhill, Ont., will take on Switzerland's Roger Federer in semifinal play Friday.
In a semifinal that was delayed twice in the first set — first by a left ankle injury to the third-seeded Halep and then by an ill woman on Centre Court during the tiebreaker — Halep double-faulted on break point in the second set and then was broken again by Bouchard to give the Canadian a 4-1 lead.
It was third time lucky for Bouchard — she had lost both previous semifinals in Grand Slam tournaments this year. She has not dropped a set in six matches so far at Wimbledon.
Kvitova is the only player born in the 1990s to have won a major title, taking the crown at the All England Club in 2011. She improved her record to 25-5 on the Wimbledon grass and she's made at least the quarter-finals five years in a row.
"I know how (it feels) when you hold the trophy so I really want to win my second title here and I will do everything I can," Kvitova said.
Bouchard, from Westmount, Que., is the only woman to have advanced to all three Grand Slam semifinals this year. She won the 2012 junior title at Wimbledon.
It was the first Grand Slam semifinal between two Czech women. It marked No. 6-seeded Kvitova's 15th consecutive win against a left-hander and she beat 23rd-seeded Safarova — who was playing on Centre Court for the first time — for the sixth match in a row.
"I don't have words to describe my feeling right now," Kvitova said. "It was a tough match mentally, as well, because Lucie is a good friend of mine. We know each (other) very well off the court and on the court, as well."
Safarova, the oldest of the four semifinalists at 27, was broken in the first game, the final two points of the game coming with two Kvitova forehand winners to an open corner. But Safarova, who had only four unforced errors in the first set and seven for the match, broke back in the fourth game, and the two stayed on serve until the tiebreaker.
With the score tied at 6-6 in the tiebreaker, Safarova's forehand error into the net gave Kvitova her second set point, and Kvitova converted it with a running cross-court winner, pumping her fist and yelling out.
Kvitova broke Safarova, who beat five-time champion Venus Williams in the third round, in the second game of the second set on her third break-point chance, then consolidated it after two deuces in the next game to go up 3-0.
She went ahead 4-1 after saving a break point in the fifth game, broke again in the sixth game and then held her serve at love in the final game. She set up match point with an ace and clinched it on a cross-court backhand in 1 hour, 20 minutes.
Kvitova saved her best for last: up to 6-all in the tiebreaker, Safarova had won more total points, 40-39. From there, though, Kvitova won 31 of the last 48 points in the match.
"I tried to be focused from the beginning of the second set when I won the tiebreak, and really I (broke) her when she was serving for the first time and I just kept it going," Kvitova said.
Safarova was playing in her first major semifinal and had been 4-8 at Wimbledon in eight previous tournaments, never advancing beyond the third round.
The men had the day off Thursday ahead of Friday's semifinals. In addition to the Federer-Raonic match, top-seeded Novak Djokovic will play Bulgaria's Grigor Dimitrov.
The winners will play Sunday in the final.
Also Thursday, Vasek Pospisil of Vancouver and American Jack Sock upset the second-seeded duo of Alexander Peya of Austria and Bruno Soares of Brazil in men's doubles quarter-final action. The third-seeded team of Toronto's Daniel Nestor and Nenad Zimonjic of Serbia dropped a 3-6, 7-6 (7-5), 6-3, 6-4 decision to fifth seeds Leander Paes of India and Radek Stepanek of the Czech Republic.
With files from The Associated Press.