Colorado was coming off a 19-2 victory Wednesday night, but it trailed 1-0 before its rally in the sixth.
Arizona left-hander Robbie Ray (3-2) hit Carlos Gonzalez and walked Chris Iannetta with one out before he was replaced by Silvino Bracho, who was called up before the game. Parra then hit a tying single to right, and Tapia followed with another single off Andrew Chafin. LeMahieu drove in Parra with a sacrifice fly.
The Rockies added two more in the seventh on Story’s 18th homer off of Randall Delgado and Gonzalez’s RBI single.
Scott Oberg (3-0) got two outs for the win.
The Diamondbacks jumped in front on A.J. Pollock’s RBI single in the first. Paul Goldschmidt and Steven Souza Jr. each had two hits.
Souza led off the fourth with a triple and hit a leadoff double in the sixth and was stranded each time. Ketel Marte, John Ryan Murphy and Ray struck out in the fourth, and Souza was thrown out when he tried to score from third on Murphy’s grounder to third baseman Nolan Arenado in the sixth.
Freeland struck out four and walked one in 5 1/3 innings.
Diamondbacks: RHP Clay Buchholz (strained left oblique) is scheduled to pitch a simulated game on Friday. Manager Torey Lovullo said Buchholz will throw 55 to 60 pitches.
Rockies: RHP Chad Bettis (blister) won’t be activated from the 10-day DL for a possible start Saturday. Manager Bud Black has not announced a starter for that day.
The Diamondbacks placed right-hander Shelby Miller (right elbow inflammation) and left-hander T.J. McFarland (strained left neck) on the 10-day disabled list and recalled right-handers Matt Koch and Bracho from Triple-A.
Miller left Wednesday’s loss with elbow tightness and was sent back to Arizona for further evaluation. It was Miller’s fourth start since returning from Tommy John surgery.
”He’s going to get an MRI,” Lovullo said. ”Holding out hope and always optimistic that it’s going to be as positive as it can be. (Wednesday) night was in a rough spot, he felt bad, but nothing he did was his fault.”
Diamondbacks: RHP Zack Godley (10-6, 4.85 ERA) will face Anibal Sanchez on Friday to start a three-game series in Atlanta.
Rockies: RHP Antonio Senzatela (3-2, 5.34 ERA) opens a three-game home series against Seattle on Friday night.