Both Enright (1-0) and the Cardinals' Jeff Suppan (0-4) went at least five innings in a game that lasted 3 hours, 53 minutes.
It's the longest nine-inning game at 5-year-old Busch Stadium, topping the previous high by 15 minutes, and was the team's longest nine-inning game of the season by 33 minutes.
Aaron Heilman worked around two singles in the ninth for his third save in seven chances.
Young was in a 1 for 18 slump and his career average at St. Louis was down to .125 before he hit his 14th homer in the fifth for a 3-1 lead that helped the Diamondbacks win on the road for the fourth time in 22 games and avoid getting swept for a ninth time. Cory Snyder is 8 for 14 against Suppan after a three-hit game.
The 24-year-old Enright was a second-round draft pick in 2007 and was 4-1 with a 2.88 ERA at Double-A Mobile, earning nod as the sub for Jackson, who threw 149 pitches in his no-hitter and is getting two extra days' rest before his next start Friday at home against the Dodgers.
Enright gave up an RBI triple to Matt Holliday in the first but otherwise frustrated the Cardinals, who stranded five runners in scoring position against the rookie, who allowed four hits and four walks and left with a 3-1 lead.
Suppan lasted 5 2-3 innings and 109 pitches, both highs for him in four starts since rejoining St. Louis. But he couldn't close out innings, with Young's homer and Rusty Ryal's RBI single in the sixth both coming with two outs.