Young was the only man to get on base for the Rockies as Miller fanned 13 in the first complete game of his young career.
Carlos Beltran went yard for the Cardinals, while Matt Holliday and Pete Kozma each drove in a run.
Jon Lester also hurled a one-hitter to lead the Boston Red Sox to a 5-0 win over the Toronto Blue Jays.
Lester allowed just on baserunner all night - Maicer Izturis doubled in the sixth - as he struck out five in his third career shutout to help the Sox end a three-game losing streak.
Daniel Nava led the Boston offence with two runs and a pair of RBIs.
Lyle Overbay had a home run and five RBIs as the New York Yankees beat the Kansas City Royals 11-6.
Ichiro Suzuki also homered, while Phil Hughes got the win despite allowing six runs in 5 2/3 innings.
Alex Cobb struck out 13 in just 4 2/3 innings before the Tampa Bay Rays beat the San Diego Padres 6-3.
Ryan Roberts and Ben Zobrist each drove in a pair, while reliever Jake McGee was credited with the win.
Angel Pagan homered as the San Francisco Giants overcame Atlanta 8-2, defeating Braves starter Tim Hudson for the first time in 10 attempts.
Hudson had been 6-0 in his last nine starts against the Giants, stretching back to his last defeat against them in 2006.
Ian Desmond had three hits including a home run, drove in three and scored three times in the Washington Nationals' 7-3 victory over the Chicago Cubs.
Manny Machado's tie-breaking RBI single led a three-run 10th for the Baltimore Orioles as they beat the Minnesota Twins 9-6.
Raul Ibanez cracked a three-run homer off Oakland rookie Dan Straily as the Seattle Mariners beat the Athletics 6-3.
Garrett Jones belted a three-run shot in the Pittsburgh Pirates' 7-3 win over the New York Mets and Brandon Phillips went yard to help the Cininnati Reds edge out the Milwaukee Brewers 4-3.
Prince Fielder and Miguel Cabrera homered in the Detroit Tigers' 10-4 win over the Cleveland Indians, while Jeff Baker's long ball led the Texas Rangers to a 4-2 victory over the Houston Astros.
The Los Angeles Angels beat the Chicago White Sox 7-5, the Arizona Diamonbacks edged out the Philadelphia Philles 3-2 and the Miami Marlins were 5-4 winners over the Los Angeles Dodgers.