LeMahieu gave Colorado the lead with his third-inning homer to left field, his second in two days. He has hit nine of his 11 homers on the road, including the shot that gave Colorado the 10th-inning lead in Saturday night's 5-3 win.
Marquez (11-9) won his fourth straight road decision. He allowed two runs on five hits and two walks in seven innings and has not lost away from home since June 14 at Philadelphia.
Marquez allowed a run in the first when Freddie Freeman doubled and scored on Johan Camargo's single. He then threw four straight scoreless innings before Camargo's single in the sixth again drove in Freeman.
The Rockies, battling Arizona for the NL West lead, completed a 5-1 road trip to improve to 37-29 away from Coors Field. They have won their last four series in Atlanta; the Braves won two of three in Colorado from April 6-8.
Sanchez allowed three runs on five hits and two walks with eight strikeouts.
Pinch-hitter Carlos Gonzalez hit a run-scoring single off Brad Brach in the ninth to drive in Ryan McMahon, who singled and moved to second on Brach's balk. Gerardo Parra, who hit a one-out single, was thrown out at third by center fielder Ender Inciarte while trying to advance on McMahon's bouncer up the middle.
Wade Davis gave up a one-out single to Inciarte but had three strikeouts in the ninth for his NL-leading 35th save.
Braves rookie Ronald Acuna Jr. was 0 for 4. His team-record streak of reaching safely in nine consecutive plate appearances leading off a game ended with his fly ball to center in the first.
The Braves, trying to protect their slim NL East lead, fell to 9-18 against the NL West this season. They are 40-19 against NL East teams.
Colorado's only previous sweep in Atlanta was in a three-game series Sept. 12-14, 1997.
Rockies: LHP Tyler Anderson (6-5, 4.39) will try to bounce back from allowing a career-high nine runs in his last start at Houston when Colorado, off on Monday, opens a three-game home series against San Diego on Tuesday night. The Rockies are 16-5 at home since July 2.