"That was great,'' manager Bud Black said. "When you get contributions from guys up from Triple-A, it really makes the club have a good vibe to it. And obviously the big swing from Parra."
Lefty Tyler Anderson (3-1) allowed four runs (three earned), seven hits and a walk, with a strikeout, over 5 2/3 innings. It was the first time he won in three career starts at Petco Park and it was his second victory in his last three decisions.
"In general, it was OK," Anderson said. "Probably too many good pitches to hit, I would say. But for the most part it was all right, at least it gave us a chance to win, battle, stay in there.''
Wade Davis, the Rockies' third reliever, pitched the ninth for his 15th save, which paces the Majors.
Bryan Shaw replaced Anderson in the sixth and surrendered an RBI single to A.J. Ellis, cutting the Padres deficit to 6-4.
Rookie Joey Lucchesi, another southpaw, received a no-decision in his third start against the Rockies. He was charged with six hits and three runs, with a walk and two strikeouts, across five innings.
The Rockies feasted on soft-tosser Kazuhisa Makita and his submarine delivery in the sixth. Ian Desmond and Chris Iannetta produced one-out singles, before Parra unloaded with a three-run shot to give Colorado a 6-3 edge.
"I was happy that we got the lead back, that was the first thing in my mind,'' he said. "It was a good homer because the momentum went back our way. We knew that we had the arms in the bullpen to keep us close and we got the 'W.'"
The ball that found the seats will find a place on Cuevas' mantle.
"It will go next to my first hit at my home in my room,'' he said.
Cuevas caught a break when a Padres fan threw back the home run ball. The Rockies didn't have to negotiate to retrieve Cuevas' momento.
"I didn't know that,'' he said. "I just saw it come back and I was hoping that the outfielder threw it in. Then one of the coaches said he had it so we're excited about it.
"I hit it good, and I was just trying to see if it was high enough, and when I saw him turn around and it hit the stands, it was a pretty electric feeling.''
Black was upbeat about the Rockies' approach at the plate. One day after striking out 15 times in a loss to the Brewers, Colorado had nearly as many strikeouts (five) as home runs.
"I want to say that was an outlier yesterday as far as the punch outs,'' Black said. "I do think our strikeouts are a little high, and we talked about that and we're going to make some adjustments.''
San Diego took its first lead in the fourth. Trevor Story sailed his throw over Desmond's head on Franmil Reyes' ground ball, with Franchy Cordero coming around the score.
The Padres tied the game at 1 in the third on Manuel Margot's run-scoring single. The inning might have been more costly, save for a great throw from Iannetta to Anderson as Lucchesi tried to score on a pitch that ricocheted off Iannetta's glove to the backstop. Iannetta pounced on the erratic pitch and fed a strike to Anderson to easily retire Lucchesi.
SOUND SMART WITH YOUR FRIENDS The Rockies have had at least three home runs in seven different games this year. What's surprising is that just one was accomplished in the thin air at Coors Field. Three times, the opponent has been the Padres, including the lone occasion Colorado did it in Denver.
HE SAID IT "I asked [Carlos Gonzalez] how many times did you feel like I felt today? He said, '220 times.' I got a ways to go. I just have to do it one at a time." -- Cuevas, on chatting with his veteran teammate after hitting his first homer in the Majors
UP NEXT Right-hander German Marquez will close out the two-game set on Tuesday afternoon, looking to rebound from a rough outing on Thursday against the Brewers. He allowed five runs and a career-high-tying 12 hits in 4 2/3 innings. Marquez pitched three scoreless innings against the Padres on April 11 before being ejected. He will oppose right-hander Jordan Lyles with first pitch at 1:40 CT.