Travis Shaw broke out of a May slump with three hits, and Lorenzo Cain homered for the Brewers, who had 12 hits.
Trevor Story homered for the Rockies, who fell to 6-9 at home this season.
Chacin (3-1), who spent his first five-plus seasons for Colorado, allowed two runs on four hits and two walks while striking out five in 5 1/3 innings. He was backed by timely hitting from his offense and a bullpen held Colorado scoreless over the last 3 2/3 innings.
Cain got Milwaukee started by hitting the first pitch from German Marquez over the wall in center to make it 1-0. In the second inning, Story's eighth home run tied the game.
The Brewers went back ahead on Manny Pina's sacrifice fly in the third inning and then broke it open in the fifth. Shaw led off with a single, and Jesus Aguilar followed with a double to put runners on second and third.
Hernan Perez's single to center scored both runners. Perez moved to third on a groundout and Chacin's soft single to third base. Cain's single drove in Perez and chased Marquez. Mike Dunn came on and struck out Christian Yelich to end the inning.
Marquez (2-4) allowed five runs and a season-high 12 hits in 4 2/3 innings.
The Rockies got a run in the bottom of the fifth when Ian Desmond led off the frame with a triple to left field and came home on shortstop Orlando Arcia's error on the relay throw.
Colorado couldn't mount any significant threat the rest of the way, and Jeremy Jeffress struck out the side in the ninth for his third save.
The Rockies are 1-2 on their current six-game homestand and have scored just six runs in the three games. They were shut out by the Los Angeles Angels 8-0 on Wednesday afternoon.
--Field Level Media
Milwaukee | Colorado | |
Jhoulys Chacin | Player | German Marquez |
Win | W/L | Loss |
5.1 | IP | 4.2 |
5 | Strikeouts | 3 |
4 | Hits | 12 |
3.38 | ERA | 9.64 |
Milwaukee | Colorado | |
Travis Shaw | Player | DJ LeMahieu |
3 | Hits | 2 |
0 | RBI | 0 |
0 | HR | 0 |
4 | TB | 2 |
.600 | Avg | .500 |