The American sent down four straight aces to close out the match and line up a semi-final against Austria's Jurgen Melzer, who battled from a set down to oust defending champion Tommy Haas 2-6, 6-2, 6-4.
While Roddick remains on course for his third title, crowd favourite Andre Agassi was knocked out by sixth-seeded Frenchman Sebastien Grosjean in three sets.
After surrendering the opening set to the two-time champion, Grosjean eased his way to a 4-6, 6-1, 6-2 quarter-final victory, his third in seven matches against the 34-year-old second seed.
Grosjean next faces Ecuadorean qualifier Nicolas Lapentti, who battled past American James Blake 6-4, 1-6, 7-6 in a night match.
Roddick paved the way to victory with a brutal display of power serving that included 14 aces and took just 57 minutes to complete.
"That's probably the best match I've served this year, so far," said Roddick, who broke Horna in the 10th game to take the opening set before running away with the second.
"I was hitting my spots," he added.
"I was getting good action and was able to hit all my serves today. I felt good about it, was in control of it and I set the tone."
The American, who has reached four consecutive finals in Hosuton, was delighted with the way he closed out the contest.
"Four aces in a row at any time is fun, but especially when you're serving it out," Roddick said.
Agassi struggled to overcome Alex Calatrava in three tough sets on Thursday and despite starting well against Grosjean, poor serving allowed the Frenchman to gain the upper hand.
"It was a good first set then he picked up his level and changed his strategy a little and started hitting it pretty high and pretty deep and I couldn't step up on it," Agassi said.
"I made some bad decisions followed by some bad swings and the second set got away and I never got it back together after that."
After losing the opening set, Melzer raised his service game to take control against Haas and sealed victory on his first match point with a sublime winner down the line.
"I have to really give him credit, he served very well, went for his shots and played steady," Haas said. "He didn't really give me many opportunities to come back."