Thiem, the 2018 Roland Garros runner-up and victor of the Barcelona title last month, prevailed in two hours 10 minutes against Federer having saved two match points in a 15-minute second set tie-break.
Djokovic outplayed Thiem in both tiebreakers at the Magic Box centre court, converting on his first match point to set up a final against Stefanos Tsitsipas.
Federer now has little time to recover to face arguably the second best clay courter in the game in Dominic Thiem who beat the Swiss to win Indian Wells.
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Thiem over-indulged in risky drop shots from deep and surrendered the first set with a limp forehand after just over an hour. Tsitsipas hopes to make his fourth final of the year and his seven final appearance of his career. The most recent match was this year in the Australian Open, a match Nadal won in 24 games. He made a decision to return this year in preparation for his first French Open appearance since 2015. He didn't play his quarterfinal match because Marin Cilic withdrew with food poisoning.
"I had to play good tennis and reach my best level".
Halep will not yield easily but Bertens has some serious momentum and she can go one better here and win the title, 12 months after losing to Kvitova in the final. After saving match points in the previous round, against Gael Monfils, Federer spurned several chances in the second set tiebreak to progress to today's semi-finals before Thiem edged the decider. He squandered five break points in the second, and then had match points at 8-7 and 10-9 in the tiebreaker before Thiem forced the deciding set by converting his sixth set point.
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The Frenchman continued to have the upper hand in the third jumping out to a 4-1 lead until Federer roared back.
The fifth-seeded Thiem outlasted Federer in the second-set tiebreaker and broke him twice in the third set to close out the match in more than two hours. Then the Swiss, thanks to some timely serve-volley artisty, saved the match points at 5-6 and rolled in the breaker.
"I'm really happy that I managed to keep my nerves down and fight back".
Thiem lost the Madrid final to Nadal in 2017 and to Alexander Zverev in 2018.
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"I really liked my fighting spirit", Tsitsipas said. "But nevertheless, if I take a step back, it's all good". It's a big challenge. "He's won the last three Slams and he is at the top of the ranking again".