Mager stunned Thiem as he defeated the current world no 4 7-6(4), 7-5 in straight sets. The match was actually scheduled to hold on Friday. But the match couldn't be completed due to bad weather conditions.
The Italian was leading 7-6(4), 2-1 when the match was suspended. And he held his nerve to finish the job on resumption of play on Saturday.
Mager held his opening three serves on Saturday to lead 5-4. He then dropped a serve but turned the tide in his favour with back-to-back winners. And the 25-year-old fired an ace out wide to seal his victory.
Thiem said he didn't deserve to win as he wasn't at his best. And he revealed his plan, which was to play more aggressively on Saturday, didn't work.
"I did not play my best tennis this week. I was trying everything. Unfortunately, I did not deserve to win. He was a better player. I have to give all credit to him, " Thiem was quoted as saying by Rio Open on Twitter.
"I had to change something of yesterday. And I was feeling I was all the time in defense, with not enough power in my strokes. And I tried to play more agressive, serve and volley, more slices. But it did not work out".
The other quarter-final tie saw Balazs beat Martinez 2-6, 6-4, 6-2 after three sets. Balazs was trailing 2-6, 2-2 before the rain on Friday. But he returned rejuvenated on Saturday to turn the match around.
Balazs broke serve six times throughout the match to reach the semi-finals in Rio.
Mager will face Balazs in the semi-finals.
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