The seventh-seeded Bouchard, who raced through the opening set in 29 minutes, ended up spending just over two hours in what turned into a battle with her Romanian opponent.
Bouchard, from Westmount, Que., and Begu spent more than an hour playing a second set littered with seven breaks of serve, with the Canadian losing a 3-1 lead and eventually the set on a double-fault.
Bouchard took a toilet break and said she gave herself a pep talk.
"I took a good long look in the mirror, and kicked myself in the butt a bit," she said. "Back on the court I relaxed and tried to play my game. I always do better when I do that.
"I felt like I started really well, I wanted to keep it going," said Bouchard. "She had some good shots and my level totally dropped— that's not really good... It's disappointing for me because I want to play so well and I want to be perfect. That's not possible. I started being a bit less aggressive, a bit too passive, and that's not my game at all.
"She could string together a few good points here and there, hit some good shots and serves and got some confidence in the second set. But I learned a lot and I'll try to make sure it doesn't happen next time."
Bouchard corrected many of her errors in the final set, breaking in the first game on the way to the win. She will now play second seed Maria Sharapova, who beat China's Peng Shuai 6-3, 6-0.
"I'm happy that I could regroup and play a bit better tennis in the third. I want to build on that for the next match."
Bouchard has lost all three of her matches against five-time Grand Slam champion Sharapova— including two at the French Open over the past two seasons.
"I think it's always great to play the best players in the world," said the Canadian. "We've had a couple matches, and a good match last year, I think I was close.
"But I've progressed a lot since then, I really want to take it to her, go for my shots. It's more fun when I play that way, too. I had more fun in the third set today. So I want to try to do that."
Bouchard, the only Canadian, female or male, to reach a Grand Slam singles final when she played Petra Kvitova at Wimbledon last summer, had never faced Begu. The 42nd-ranked Begu upset ninth seed Angelique Kerber in the opening round.
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