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The defending champion secured a 6-2, 2-6, 6-1 victory in his quarter-final clash with Baez, who he defeated at the same stage in last year’s competition.
A strong third set saw Norrie reach the semis in Lyon for a fourth time and he was pleased with his confidence going into that decider.
“The second set he came back strong, he was winning the tougher games like I was in the first set,” Norrie told the ATP website.
“I tried to reset and came out with a lot of energy.
“I have won a lot of three-set matches this year, so I had a lot of confidence going into the decider and I thought it was a solid match.”
The victory sets up a semi-final against Francisco Cerundolo, who defeated Norrie’s fellow Briton Jack Draper 4-6, 6-4, 6-3 on Thursday.