Quintana, acquired Thursday in a blockbuster trade with the crosstown White Sox for four minor league prospects, dazzled the Orioles over seven scoreless innings, striking out 12 and allowing just three hits in the process.
The Cubs provided more than enough support with their bats, scoring four runs in the second inning off of maligned Orioles starter Ubaldo Jimenez.
Catcher Willson Contreras, batting cleanup, recorded the first four-hit game of his career, while Anthony Rizzo and Kris Bryant each homered for the defending World Series champions.
The Cubs (46-45) earned their first interleague sweep on the road since August of 2016 and just their second road sweep over an American League East opponent with a big assist from their newly acquired pitcher.
Quintana, who had struggled in six previous starts against the Orioles, matched the Cubs' record for the most strikeouts in a debut. It marked the third time this season that the left-hander has struck out 10 or more batters and the 10th time of his career. His career high for strikeouts in a game is 13.
Adam Jones registered the first hit off Quintana as a Cub with a ground-rule double to start the bottom of the fourth. However, the Orioles stranded him on third-base after a meek ground out to first by Manny Machado and strikeouts by Jonathan Schoop and Mark Trumbo.
Quintana was 1-4 against the Orioles with a 4.29 ERA. In a May 7 start for the White Sox, he allowed four runs on nine hits to the Orioles over five innings in a losing effort. But he showed Sunday why he could be such a valuable addition for the Cubs during the second half of the season.
Jimenez, on the other hand, was not nearly as good for the Orioles. The Cubs jumped all over him with three straight doubles to start the second inning and grab the early lead.
A two-out single to center by leadoff man Ben Zobrist in the second made it 4-0 and marked the 10th two-out run the Cubs had scored over the last two games.
Bryant extended the lead to 6-0 in the fourth by ripping a 1-0 pitch from Jimenez into the left-field stands for his 19th home run of the season. Later, with no outs in the ninth inning, Rizzo belted his 22nd homer into the center-field seats.
Over the course of the three games in Baltimore, the Cubs scored 27 runs and hit 10 home runs.
Jimenez (4-5) lasted just 3 2/3 innings, allowing six earned runs on 11 hits. He hasn't made it out of the fourth inning in six of his 14 starts this season. He hasn't gotten past the fifth inning in 10 of those starts.
The Orioles, meanwhile, fell to a season-worst seven games below .500 at 42-49.
NOTES: After losing six consecutive road series, the Cubs are now unbeaten in four of their last five. ... C Willson Contreras has now hit safely in 10 of his last 11 games. ... LHP Jose Quintana is the first left-hander and third overall pitcher to makes starts for the Cubs and White Sox in the same season ... RHP Ubaldo Jimenez suffered his first home loss of the season in seven starts. He fell to 8-4 in 15 interleague starts for the Orioles and 15-11 in 33 starts overall against the opposing league. ... The Orioles were swept at home for just the second time this season. They lost three in a row at home to the Minnesota Twins on May 22-24.