Defending Lyon Open champion Cameron Norrie progressed to the semi-finals of the clay tournament on Thursday, but Jack Draper missed out on an all-British affair in the final four.
Aiming to advance to the showpiece event in Lyon for the third year running, Norrie took one hour and 51 minutes to see off Baez and proved too hot to handle in the opening exchanges.
The British number one raced into a 3-0 lead, and after squandering two chances for the double break in the sixth game, he made no mistake in the eighth to put one foot in the semi-finals.
However, Baez came back with a bang in the second set, immediately breaking Norrie and saving two break points in the third game as the Briton's serve began to let him down.
A pair of double faults from Norrie allowed Baez to earn the double break in game seven to take the match to a decider, but the world number 14 quickly rediscovered his groove, winning six games from seven in the third set to continue the defence of his crown.
"The second set he came back strong. He was winning the tougher games like I was in the first set. I tried to reset and came out with a lot of energy," Norrie said on the court. "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."
Norrie could have been facing a semi-final against compatriot Draper, but the 21-year-old capitulated in his battle with another Argentine in Cerundolo, who impressively fought back to prevail in a two-hour and 29-minute contest.
With plenty of big forehands early doors, and a few double faults from Cerundolo, Draper broke in the seventh game and sealed the first set with an ace before passing up four opportunities to break Cerundolo's serve in the opening game of the second set.
The Argentine wasted three such chances of his own before Draper once again broke in the seventh game, but Cerundolo dug deep to win three games on the spin as the contest went the distance.
Fewer and fewer first serves were landing for an increasingly frustrated Draper, who fell 3-0 down in the deciding set and could not find a way back, saving two match points on serve before a long backhand return sealed the win for Cerundolo.
The world number 28 will now gear up for a third meeting with Norrie in the semi-finals, having lost to the holder in the second round last year before knocking the Briton out of the Monte Carlo Masters in straight sets last month.