The Rockies prospect gave up three hits and a walk while striking out seven over seven innings as the Double-A Tulsa Drillers blanked the Hooks, 6-0.
"This is in the top five starts of the year," Frazier said. "It wasn't my best one, but it's one to learn from and go from there.
"I had excellent command with my fastball. If I missed strike one, I was able to throw my curveball and slider for a strike. Then I really found my changeup later in the game. I got stronger as the game went on."
The 2007 eighth-round pick stranded two runners in scoring position in the first inning by recording back-to-back strikeouts of rehabbing Astros outfielder Justin Maxwell and top prospect Jonathan Singleton.
Frazier (4-9) set the side down in order in the second and he faced the minimum in the third after Jonathan Villar -- who ripped a one-out double to center field -- was caught stealing third.
Jose Martinez doubled leading off the fourth, but Frazier retired his final 12 batters before turning over a 6-0 lead to the bullpen.
"I was done after seven," the 23-year-old right-hander said. "I threw too many pitches in the first and second innings. If I had thrown as many pitches in the first two as I did in the last five, I might have had a chance. I've been going six or seven innings and 85 or 86 pitches. Tonight my 96 pitches was the highest all year.
"They had Jonathan Singleton in their lineup and he was in the Futures Game, and they had Justin Maxwell rehabbing for them, but I attacked it the same way. I just had to keep going at them. I learned that if I remember to pitch to contact I can get outs, no matter who is at the plate."
Frazier lowered his ERA to 3.74 and won for only the second time in his last 11 starts. Over his previous 10 games, he was 1-6 with a 5.24 ERA.
Last time out, Frazier yielded two runs on four hits over six innings against San Antonio. But the outing before that, he surrendered five runs on 10 hits in six innings against the same lineup.
"Bad luck really singled me out," said Frazier, who attended Bishop Kelley High School in Tulsa, Okla. "I gave up a two-run homer in the third inning and then everything was single, single, single. A ball got lost in the lights and then a ball hit off the first base bag."
Frazier entered Tuesday's game having faced every Texas League club, except the Hooks.
"They hadn't seen me, so that was good. They'd seen every one else in the rotation and I have a different delivery from most of them," he said. "I pitch a little quicker and I keep that tempo so I don't give the hitter a chance to see what is coming next. It's a huge advantage.
"I just have a little more deception. I have a really fast front side and a quick arm. I don't necessarily have the smoothest delivery, but it is deceptive."
Frazier got help from Rockies No. 16 prospect Kent Matthes, who went 3-for-4 with two homers and a season-high four RBIs. Ben Paulsen also had three hits, including an RBI triple.
"He's been working really hard in the cage," Frazier said of Matthes. "We bunt and swing off the machine in there and I see him working hard every day. He was not necessarily trying to fix anything, just working on taking things one at-bat at a time. Tonight might just be the night that starts him back off."
Matthes, the 2011 California League MVP, was hitting .191 with nine homers and 27 RBIs in 77 games before notching his second multi-homer game of the season.
"The whole year has been a struggle," admitted Matthes, who said he's changed his approach to focus on hitting gap-to-gap and using the middle of the field. "Coming off [left] hand surgery when I was hit by a pitch in August, I couldn't grip a bat for three months. Since then, I've been trying to find my swing.
"There have been a lot of ups and downs. I've been experimenting with new stuff and trying to get back to the things that made me successful last year. You can't get caught up in stats; you just have to work on the progress and not focus on the results."
Will Harris worked around a hit and a walk in the eighth and Josh Sullivan fanned one in a hitless ninth to wrap up the Drillers' fifth shutout.