"I feel really good," Miller said. "It's definitely the best game I've thrown in my life. How it finished was unbelievable. It was a great experience. Yadi (catcher Yadier Molina) was calling a great game and they were making great plays for me. It was a start I'll remember the rest of my life."
Miller (5-2) struck out Young to end it with his 13th K, tying a Cardinals rookie record.
Young felt fortunate just to reach base at all.
"It was a jam shot and I just put it in a good location," Young said. "I was just fortunate enough to find grass.
"He was working both sides of the plate, using his fastball. He had great command," Young added. "His battery mate back there is obviously one of the best game. It was a good combo for them."
Miller agreed with Young's assessment of Molina.
"I say it time and time again, what Yadi calls, I throw," Miller said. "He was calling the right thing all night. He's done a terrific job all year and he's helping me out tremendously. I'm happy he's my catcher, that's for sure."
The one-hitter was the fewest hits allowed by a Cardinals pitcher since Bud Smith tossed a no-hitter on Sept. 3, 2001, and it was the second one-hitter of the night in the major leagues. Boston's Jon Lester was perfect until he allowed a two-out double in the sixth against Toronto.
In a near-perfect performance, Miller threw 113 pitches.
"It's pretty incredible," St. Louis manager Mike Matheny said. "How he held his composure, made real good pitches all night long against a very good offense."
Miller lowered his ERA to 1.39, which is the lowest for a Cardinals pitcher in his first eight starts since Howie Pollet had a 2.09 ERA in his first eight in 1941.
Carlos Beltran hit a solo homer -- his ninth -- for St. Louis. Pete Kozma added an RBI single and Jon Jay a sacrifice fly for the Cardinals, who are National League-best 22-12.
Molina had two hits to extend his hitting streak to 10 games, which is the longest for a Cardinal this season.
Rockies starter Jon Garland (2-3) gave up all three runs in five innings. Garland allowed seven hits and three walks while striking out five.
Garland retired the first five batters he faced before Jay singled to center with two outs in the second. David Freese walked, and Kozma drove home Jay with a single to left.
Beltran made it 2-0 when he hit Garland's first pitch of the third inning 409 feet into the seats in right. Jay gave the Cardinals a three-run cushion with a sacrifice fly in the fifth.
Dick Hughes and Scipio Spinks also struck out 13 for the Cardinals as rookies. ... Molina is batting .461 (18 for 39) during his hitting streak. ... Colorado has not won a series in St. Louis since sweeping four games from June 5-8, 2009. ... Jay extended his hitting streak to seven games with his second-inning single. ... Garland is 1-6 with 6.61 ERA in his career against St. Louis. ... Former Cy Young award winner Chris Carpenter took another step toward possibly returning to the mound by tossing a pain-free bullpen session. The 38-year-old's career appeared as if it may be over when it was announced in February that he was unlikely to pitch in 2013 because he was still experiencing chronic pain in his neck, shoulder and arm. Friday's bullpen session was the fourth for Carpenter, who tossed about 70 pitches.
37,800 (86% full) - % is based on regular season capacity
61 degrees, cloudy
Home Plate - Mike Everitt, First Base - Marty Foster, Second Base - Scott Barry, Third Base - Tim Welke
Friday May 10 was the first day in modern baseball history (since 1900) in which 2 pitchers threw shutouts allowing 1 hit or fewer while walking 0 batters on the same day.
From Elias: Shelby Miller threw a 1-hit shutout with 13 K and 0 BB and he's just 22 years old.
He and Kerry Wood (in his 20-K game against the Astros) are the only pitchers in MLB history to do that at 22 or younger.
From Elias: Shelby Miller is the 1st Cardinals pitcher in the modern era (since 1900) to throw a shutout with 1 hit or fewer and no walks and at least 13 strikeouts.
Shelby Miller had a Game Score of 97, the 2nd-highest by a Cardinals pitcher that went 9 IP or fewer in the Live Ball era (since 1920).