"He's got good stuff and located the ball well," said Ross, who is 5-for-11 with five RBIs against Hellickson.
"His changeup is as good as it gets, and he lives and dies with it. There are just certain guys you time up well and certain guys you don't. I've hit him well the last two games but not as much before that."
Ross has hit safely in six of his past eight games, batting .452 (14-for-31) over that span.
"He's barreling the ball a lot better," Arizona manager Kirk Gibson said. "You can see that coming on. He's much calmer at the plate and not jumping at the pitch."
Ross' eighth home run came moments after Eric Chavez doubled home Paul Goldschmidt to tie the game 1-all in the fourth. Hellickson then walked Aaron Hill before Ross homered to left to make it 4-1 one pitch after fouling a ball off his right calf and falling to the ground.
"You can't walk the leadoff guy in an inning," Hellickson said. "I still could have limited the damage a little bit. I fell behind to Chavez and couldn't make a good pitch when I needed to."
Hellickson (10-5) failed to pitch past the fifth inning for the second straight outing for the Rays, both against the Diamondbacks.
Hellickson gave up five runs, five hits and three walks, hit a batter, and struck out one as the Rays slipped 1 1/2 games behind Boston in the AL East.
It was Hellickson's first road loss since April 25 against the Chicago White Sox.
Miley (9-8) allowed one run, struck out five and walked two for his fifth win in his past six starts.
"You want to get a good rhythm going," Miley said. "That's when you have success. Earlier, I was getting upset with myself after one or two small mistakes, and it's kind of snowballed. I get too quick and I'm just firing it up there, no mindset, no thought."
Chavez finished with a pair of RBI doubles for the Diamondbacks, who pulled within five games of the Los Angeles Dodgers in the NL West.
"We just have to put runs on the board more," said Chavez, who has seven RBIs in three games against the Rays this season.
Tampa Bay went ahead 1-0 on Evan Longoria's 22nd home run with one out in the fourth.
Arizona added a run in the fifth when Hellickson walked Goldschmidt and Chavez doubled off reliever Jamey Wright.
"We had a lot of hard outs," Rays manager Joe Maddon said. "We hit some balls hard for outs. I like our approach better versus Miley tonight, but the four-spot did hurt."
Tampa Bay was making its third trip to Arizona and first since 2007. ... Before the game, the Rays placed Desmond Jennings on the 15-day disabled list retroactive to Aug. 4 with a small fracture in his left middle finger. Tampa Bay selected OF Jason Bourgeois from Triple-A Durham to replace Jennings. ... The Rays also moved RHP Alex Cobb, out with a concussion, to the 60-day disabled list from the 15-day DL. ... Miley has allowed eight runs in his past seven starts to lower his ERA from 4.55 to 3.56. ... Hellickson singled in the fifth, his first career hit. ... Heath Bell, who pitched the eighth, has posted 11 consecutive scoreless outings spanning 11 1/3 innings with 15 strikeouts. ... RHP Chris Archer (6-4) will attempt to get back on track Wednesday when he faces LHP Randall Delgado (4-3) and the Diamondbacks. Archer allowed four runs in his previous start, against San Francisco, matching his total for the month of July. Delgado has allowed three runs or fewer in eight of nine starts.