McCutchen drove a two-run shot to right field in the third inning then added an RBI-double in the fifth off Edwin Jackson (4-6).
Charlie Morton (3-7) allowed one run over seven innings to win for the third time in his last four starts after beginning the season 0-6. Ike Davis hit his fifth homer of the season while Starling Marte broke out of a lengthy slump with three hits.
Starlin Castro went 3 for 4 with his eighth home run and two RBIs for the Cubs. Jackson surrendered four runs in six innings and is 1-4 since April 30. Chicago fell to 10-22 on the road, the worst mark in all of baseball.
It wasn't exactly the best way to start a 10-game trip for the Cubs, who were coming off a successful 5-1 homestand that included the team's longest winning streak in more than a year.
Any momentum generated at Wrigley Field vanished on a night Morton avoided the control problems that have plagued him much of the season. The right-hander came in with a major-league high 13 hit batters while averaging nearly 2.5 walks per start.
There were no such issues against Chicago. The Cubs needed a grounder deflecting off the glove of shortstop Jordy Mercer to extend the sixth inning before finally scoring on Castro's long double to right.
All the run did was bring Chicago within 4-1, with most of the damage done by McCutchen.
Marte, who began the night 0 for his last 23, doubled home Pedro Alvarez to give the Pirates the lead in the first. McCutchen pushed it to 3-0 in the third when he patiently waited as Jackson worked him away before reaching out and sending a pitch into the first row of seats in right for his fourth homer this month.
McCutchen nearly did it again two innings later, lacing a double off the wall in right to score Travis Snider and give Morton all the cushion he would need. Bothered by some bad luck early in the season, Morton lowered his ERA to 3.14 and struck out seven. He has 16 strikeouts over his last two starts, a significant bump for a pitcher who relies on a heavy sinker to get groundball outs.
NOTES: Pittsburgh scratched 2B Neil Walker shortly before the first pitch with what the team called an "abdominal strain." Josh Harrison moved to second and went 0 for 3, with Snider replacing Harrison in right. ... Pirates RHP Gerrit Cole threw 25 soft-toss pitches on flat ground before the game. Cole, who leads the Pirates with six victories, was placed on the DL on Sunday with what the team is calling right shoulder fatigue. ... Chicago RF Ryan Sweeney made a rehab start for Class A Kane County on Monday night. Sweeney went on the DL May 3 with a right hamstring strain. ... The series continues Tuesday. Travis Wood (5-5, 5.04 ERA) starts for the Cubs against Francisco Liriano (1-6, 4.54). Wood is 2-4 with an 8.04 ERA on the road this season.