That unsafe approach paid dividends as she hit a crosscourt forehand victor then a backhand down the line to break for 5-2 in the decider. She served out the match at love.
Halep, who is seeded third, had taken the first set 6-4.
Mladenovic appeared to deal better with the initial delay.
The match was delayed twice by rain, once with Wozniacki leading 6-4, 2-5, and the second time with Wozniacki leading 2-1, on serve in set three. The Swiss won a 22-stroke rally with a backhand smash, Mladenovic came back from two break points with another wonderful rally, and would battle though four deuces and another break point before Bacsinszky fired a cracking backhand victor to edge the break. The Swiss player then won 12 of the 15 points before rain started falling again.
A string of unforced errors from Ostapenko gifted Wozniacki a commanding early lead, although the Dane did need to save five break points on her way to establishing a 5-0 lead.
Latvian Jelena Ostapenko claimed a shock win over former world number one Caroline Wozniacki on Tuesday to book a semi-final spot at the French Open.
Because of the rain quarterfinal matches in the top half of the tournament lasted for more than five hours.
Chelsea monitoring Riyad Mahrez as Antonio Conte considers wide options
Antonio Conte's side are looking to build on a title winning summer and have been linked with a number of big-money moves. Sandro would provide Spanish defender Marcos Alonso with competition for a starting spot in Conte's team next season.
It was clear from the start that Ostapenko was going to be the aggressor and she edged a first set in which she hit 21 winners.
She is the first unseeded woman to reach the French Open final for 34 years.
The 27-year-old Bacsinszky broke French hearts in the other quarter-final as she beat 13th seed Kristina Mladenovic 6-4 6-4. She did manage to turn things around by the time the rain came, and held a sizeable lead as they headed to the dressing room for what turned out to be a three hour and 20 minute delay.
The year before that, she lost in the first round of French Open qualifying.
They're friends, played doubles together at a tournament last season, and both happen to be celebrating birthdays on Thursday: Ostapenko's 20th, Bacsinszky's 28th. Both women's quarter-finals required three separate sessions to reach a conclusion, while the scheduled men's quarter-finals - Novak Djokovic against Dominic Thiem, and Rafael Nadal against Pablo Carreno Busta - had to be postponed until 11am local time on Wednesday.
Because of showers and heavy wind much of the afternoon, the two men's singles matches on Tuesday's schedule have been moved to Wednesday: No. 4 Nadal vs. No. 6 Dominic Thiem.
Take it back further and add in hard courts: Murray was only 16-7 all season entering Roland Garros. Djokovic is the defending champion.
It is the first major since the 1979 Australian Open where no women's quarterfinalist was a Grand Slam champion.
The tournament hopes to be able to resume those before the day is done.
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