Roared on by a fervent Bulgarian contingent in the O2 Arena crowd, Dimitrov responded well to the setback, an excellent stop volley seeing him secure the first break of the third set to lead 4-3.
Dimitrov will play Nadal on Wednesday if the Spaniard beats David Goffin later today, and he will be full of confidence after producing some great net play and battling through after Thiem made his second set comeback.
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To do so, he will have to calm his nerves.
In a tight second set, the 26-year-old earned a potentially decisive break point in the 11th game but Thiem, whose service numbers improved significantly, held firm and went on to break to love in the next game to level the match.
"It, for me, was just one of those new experiences that I think I'm going to remember for the rest of my life, I think appreciate for the rest of my life", Dimitrov said. "You come in and feel the weight on your shoulders, in a positive way".
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Serving for the match at 5-4, however, he wobbled again as a framed backhand beyond the baseline allowed Thiem a reprieve.
Instead of sending the match in the tie break, Dominic played an bad service game to get broken again and fell 6-5 behind, hitting costly double faults to reduce his chances, and Dimitrov sealed the deal with a solid hold in game 12.
Consecutive double faults in the following game saw the Austrian lose serve again - this time to love.
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