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.
Brandon Nakashima reached the other semi-final with a 6-3 7-6 (4) win against third seed Tommy Paul and he comes up against Arthur Fils who reached the final four when Felix Auger-Aliassime withdrew due to a shoulder injury.
In the Geneva Open, Nicolas Jarry knocked out two-time champion Casper Ruud in the quarter-finals with a 3-6 7-6 (2) 7-5 victory and will now face Alexander Zverev, who reached the semi-finals after opponent Wu Yibing was forced to retire.
Taylor Fritz also reached the semi-finals with a 6-1 6-2 win against Ilya Ivashka to set up a clash with Grigor Dimitrov, who fought back to defeat Christopher O’Connell 6-7 (5) 7-5 6-4.