Delgado went 3.2 innings, allowing five hits, four earned runs and two homers in an 8-6 Arizona victory.
Carlos Quentin hit a solo shot off of Delgado in the second, while teammate Yonder Alonso connected on a solo blast one inning later.
"I was feeling pretty good, but had a couple bad pitches with command or something, but I feel great," Delgado said following his outing.
Delgado threw 74 pitches in his second Cactus League start, 40 for strikes. The two pitches that were hit out of the ballpark were both fastballs, and the D-backs hurler wasn't too pleased with the location of either.
"A little bit up, perfect for hitters," he said.
Manager Kirk Gibson summed up his starter's performance.
"He got through it, he got behind in counts and gave up the home runs," he said. "But he threw the ball well, he did good."
Delgado was staked to a three-run lead before he ever toed the rubber thanks to first-inning RBI singles from Martin Prado and Matt Tuiasosopo.
The game was tied 5-5 after six innings, but the D-backs broke it open with three in the seventh on RBI doubles by Aaron Hill and Paul Goldschmidt and a Tuiasosopo sacrifice fly.