In the first Enright allowed a run on a pair of hits and a walk and when he left the field after the third out Kelly Johnson told him to pick it up.
"A little lethargic, I came out with bad tempo in the first inning," Enright said. "It got better from there. Obviously, you're not going to have your best stuff at least 50 percent of the time during the year, so you have to learn to throw when you don't have your best stuff."
Enright, who allowed two runs on four hits with four strikeouts in five innings on Sunday, is battling with Armando Galarraga and Aaron Heilman for the final two spots in the rotation.
"No question about it," D-backs manager Kirk Gibson said when asked if Enright was putting together a strong case to win a spot.
In five starts this spring he has yet to allow more than two runs in a game, the only D-backs starter that can say that.
"It's not something I'm not trying to worry about right now," Enright said. "Just like I've said the whole time, that word compete, I'm just going to keep doing it until they take the ball out of my hand. I feel confident that I'm going to be here, I want to be here, I think we have something special here. I like being the underdog and being able to sneak up on people."