McCutchen hit a solo home run to left field to start the scoring in the fourth inning and then came through with another shot to the bleachers with Josh Bell on base in the eighth.
The pair of round-trippers gave McCutchen 11 for the season and continued a hot stretch that started after he got two days off, made a mechanical adjustment and was moved to No. 6 in the batting order.
Since getting back in the lineup May 26, McCutchen has gone 25-for-63 (.397). His batting average has climbed from a season low of .200 on May 23 to .255.
"I had two very productive days in Atlanta," McCutchen said, referencing his down days before the hot streak. "I had two days where I was really able to get myself where I needed to be as opposed to trying to get where I needed to be before the game and then taking it out there in the game."
Jaso came through with a two-run pinch-hit homer that also scored Jordy Mercer in the seventh inning. It was Jaso's fourth home run and second pinch-hit home run of the season. He is hitting .400 (6-for-15) as a pinch hitter this year. The reason for so much success at pinch hitting?
"I don't know," Jaso answered. "I just get ready during the game, stretch out and relax. I don't want to get too amped up or anything like that. I've done it a lot in my career. I know that nerves can get in there and adrenaline, so just keep that calm and it becomes another at-bat like you started the game."
Jaso was pinch hitting for Gerrit Cole, who earned the win (4-6). Cole snapped a four-start streak of subpar performances by throwing seven three-hit innings and allowing just one run.
"I liked the domination of the bottom of the zone early," manager Clint Hurdle said. "I liked the way he used his fastball. I liked the way he mixed in his off-speed pitches. He executed pitches. He stayed on point. He stayed on the aggressive side."
In the fifth, Colorado's Trevor Story walked and scored from first on a single to shallow left field by Tony Wolters. Story was running on the pitch and never stopped, getting to home plate right as the relay throw came from shortshop Jordy Mercer to catcher Elias Diaz. But Story snuck his hand around Diaz and touched home plate to tie the game.
"(I) got a good jump," Story said. "It helped that I was in motion. Kind of picked up the ball and saw that it was in no-man's land. We talk about that all the time. We run until (third-base coach) Stu (Cole) stops us. I could get the sense that it might have been one of those plays."
Story also drove in Mark Reynolds with an RBI single in the ninth off Pirates reliever Felipe Rivero.
Tyler Chatwood went six innings, allowing just the McCutchen home run. He struck out five and allowed six hits. Adam Ottavino took the loss (0-1).
NOTES: Pirates C Chris Stewart has been performing baserunning drills in Pittsburgh as he returns from a strained left hamstring. Stewart has been on the disabled list since May 30. ... Rockies LF Gerardo Parra will be out longer than expected with his right quad strain. Parra last played on June 6 and was originally expecting only a two-week absence... Colorado LHP Tyler Anderson threw a three-inning, 52-pitch simulated game without any pain in his inflamed left knee. The club is still deciding whether he needs to have a rehab start. He hadn't pitched since his last start May 30. ... RHP Jon Gray, who was Colorado's Opening Day starter, will make a rehab start with High-A Lancaster (California) on Wednesday. Gray has been out since April 14 with a stress fracture in his right foot.