Vargas (4-1) did not allow a hit until the fourth inning and did not allow a run until Drew Stubbs belted a two-run homer to left in the seventh that made things interesting.
Louis Coleman got the Royals out of the inning without any more damage, and Kelvin Herrera worked a perfect eighth before Greg Holland survived a shaky ninth for his 10th save.
After giving up a one-out single to Carlos Gonzalez and walking Nolan Arenado, Holland got Justin Morneau to hit a grounder to second. The ball was fielded cleanly and Kansas City got the runner there, but Morneau barely beat the throw to first base to keep the game going.
Holland promptly struck out Stubbs to leave the tying run on third base.
Jhoulys Chacin (1-1) allowed the three runs that Moustakas drove in but otherwise pitched well for Colorado. He allowed seven hits and two walks over six gritty innings.
The Rockies came into the two-game series swinging the best bats in the majors, but they were silenced by some stingy pitching. James Shields was their foil in a 5-1 Royals victory in Tuesday night's opener, combining with the bullpen on a 12-strikeout performance.
Vargas was just as tough, striking out a season-high eight in 6 2-3 innings.
One of those strikeouts proved to be especially important: Troy Tulowitzki was left looking at a called third strike in the fourth inning. The leading hitter in the major leagues argued with plate umpire Dan Bellino over the location, which appeared down and in, and continued their one-sided conversation when he had reached the dugout. Bellino responded by ejecting him.
D.J. LeMahieu took his spot in the lineup. And when the Rockies had runners on the corners in the sixth, it was LeMahieu rather than Tulowitzki at the plate. He struck out to end the inning.
The Royals had won once in 18 games when scoring three runs or fewer this season. A big reason for their anemic offense had been Moustakas, who entered hitting .147 and who had been the subject of much speculation regarding his future in the big leagues.
Royals manager Ned Yost gave the former first-round pick a vote of confidence this week, though, and Moustakas responded with his bases-clearing double in the second inning and another double in the fourth. He also hit a ball to the warning track in the sixth.
NOTES: Royals LHP Bruce Chen (bulging disk) threw a brief side session before the game. He will need at least one more before the team considers a rehab assignment. ... The Rockies are off Thursday before starting a three-game set against San Diego. RHP Yordano Ventura starts Thursday for Kansas City in the opener of a four-game series against Baltimore.