Marquez (2-2) gave up one run on four hits and a walk to win his second straight start. Mark Reynolds added a two-run single for Colorado, which won its 13th road game of the season. The Rockies are tied for second in the majors in road wins behind Houston's 15 and trail only Houston in overall wins this season with 26 victories.
Greg Holland finished his 18th save in as many chances by striking out Brian Dozier after two runners reached with two outs against reliever Mike Dunn.
Minnesota's Ervin Santana wasn't as sharp and gave up five runs in seven innings. Santana (6-2) allowed more than one run for just the second time this season and saw his ERA rise from a league-leading 1.50 to 2.07, third in the AL.
The two teams were rained out on Wednesday, leading to the day-night doubleheader. Colorado right-hander Tyler Chatwood (3-5, 5.25 ERA) starts against Twins right-hander Jose Berrios (1-0, 1.17) in the second game scheduled for 6:10 CT.
Santana entered the game with the standout numbers, but the 22-year-old Marquez outpitched his veteran counterpart.
Minnesota had two hits in the first but the runners were left stranded by Marquez. He stretches his scoreless innings streak to 15 innings before the Twins scored one in the fifth as Eddie Rosario tripled and was driven in on a sacrifice fly by Dozier.
Marquez, filling the rotation spot for the injured Jon Gray, had thrown eight scoreless innings to beat the Chicago Cubs in his last outing when he took a no-hitter into the seventh inning. Marquez retired 12 of 13 batters he faced at one point.
Arenado gave Marquez an early lead with his 10th homer this season, a first-inning shot to the second deck in left field. Arenado is hitting 16-for-31 (.516) with five doubles, four homers and 13 RBIs in the first inning this season.
Reynolds' single plated Tony Wolters and Charlie Blackmon in the third inning. Ian Desmond followed with an RBI single, but Reynolds was thrown out at home by Minnesota right fielder Max Kepler.
Blackmon added another run with an RBI single in the fourth, his second hit of the game.
Santana recovered to retire nine of the last 10 batters he faced over his final three innings.
NOTES: Colorado manager Bud Black said SS Trevor Story (left shoulder strain) would start a rehab assignment with Triple-A Albuquerque on Friday. Story has hit with the team and fielded ground balls to test his non-throwing shoulder and had no issues. ... Minnesota manager Paul Molitor said LHP Adalberto Mejia would be recalled to fill the open spot in the team's rotation and start on Saturday. Mejia started the season with the Twins, going 0-1 with a 5.79 ERA in three starts as a rookie. ... Colorado recalled RHP Carlos Estevez from Triple-A as the 26th player for the doubleheader, while Minnesota recalled RHP Drew Rucinski. ... Wednesday's rainout was the fourth this season for the Twins and the second at home. They have played the fewest games in the majors. ... The Rockies travel to Cincinnati for a weekend series against the Reds. Minnesota hosts Kansas City.