The Spanish winner benefitted as his French opponent dropped serve seven times.
For what will be his second semi-final of 2016, Carreno Busta will next face either second seed Nick Kyrgios or experienced Spaniard Nicolas Almagro with the title at stake.
The Spaniard constructed his second straight victory over France's Paire to put himself into possible title position after reaching the Sao Paulo final last February, where he lost to Pablo Cuevas.
Paire made a brief last stand by breaking his opponent while Carreno Busta served for victory, but the triumph was short-lived as the 50th-ranked Iberian broke straight back to complete the job in 73 minutes.
The Spaniard, who is seeking the first trophy of his career, denied Paire a first ATP semi-final since Tokyo more than six months ago.
Carreno advanced with modest form, striking five double-faults and finding a mere three aces. He lost serve on four occasions.
Australian crowd-pleaser Kyrgios, whose casual approach to his tennis belies his dangerous form, will be bidding to surpass his Estoril showing from 2015, when he lost the final to Frenchman Richard Gasquet.
Since that disappointment, the player, who turned 21 this week, has earned a breakthrough title in Marseille two months ago, and now stands 20th on the ATP.
Kyrgios will be playing his fourth semi-final of 2016 having stepped onto clay for the first time this year.