Eovaldi, who flashed a fastball as high as 99 mph, struck out six and allowed two runs in six innings to collect the win. Steve Cishek captured the save, his first of the season. Dating back to last year, the sidearm-throwing right-hander has converted 30 straight save chances, extending his franchise record.
Over his career, Eovaldi has had just 2.83 runs of support, the lowest average among MLB starters with a minimum of 45 starts since 2011.
"This is a completely different team," Eovaldi said. "We added the key guys we needed to add. In Spring Training, it was the same thing. We had great games in Spring Training and carried it over into the season."
The Marlins are 2-0 for the first time since winning their first four to open 2009, the club's last winning season.
A year ago, Miami was blanked in its first two games at Washington. Now it has 14 runs through two games, and Eovaldi was the recipient of just enough production.
"We talked about the run support thing last year," Marlins manager Mike Redmond said. "Sometimes that happens with some guys. I don't know if you can figure out why some guys get runs and some guys don't. Last year, he didn't get a ton of them. It was nice to go out there and keep battling. We had some great at-bats."
Miami manufactured all of its runs, with three earned, off lefty Brett Anderson.
"For the guys to come back and get the lead back was awesome," Eovaldi said. "Yesterday, we came out swinging. Today, we put up some good at-bats and we got the hits when we needed them. It was huge."
The Rockies closed the gap to one run in the eighth inning on back-to-back doubles by Michael Cuddyer and Carlos Gonzalez off Mike Dunn. But with two outs and runners on the corners, A.J. Ramos struck out Nolan Arenado.
"Last year, we were inexperienced as a pitching staff, but we showed our talent was good enough to perform," Ramos said. "Now, we've got another year under our belt. We're a little more confident. We've figured out a few more things from last year. We're kind of using our knowledge from last year and using our talent and also learning in every game."
The Marlins gained a two-run edge in the sixth inning, capitalizing on DJ LeMahieu's throwing error, which accounted for one unearned run. Reed Johnson led off with a pinch-hit double, and he moved to third on Christian Yelich's groundout to short.
Anderson used some unconventional strategy from there, by pitching around Jeff Baker to get to Stanton. The reason was because of Baker's previous head-to-head experience against the lefty.
With runners on the corners, Stanton chopped a grounder near the third-base line. Colorado forced out Baker at second, but LeMahieu's throw to first sailed wildly. Stanton was awarded second on the error.
"There probably won't be too many times where the person in front of Giancarlo Stanton gets pitched around," Anderson said. "But I faced Baker quite a few times in the American League, and he had pretty quality at-bats against me before. I liked where I was against Stanton. I felt like I'd get a groundball. Unfortunately, it wasn't hit hard enough."
Johnson scored the go-ahead run on Stanton's RBI fielder's choice. Stanton stole third and scored on McGehee's single to center.
One of the early-season story lines to follow for the Marlins is how lefty-hitting first baseman Garrett Jones does against southpaws. For the second straight game, he had a chance. After going hitless in four at-bats with a walk on Opening Night, Jones delivered a second-inning single to center that set the stage for a two-run inning.
Jones scored from first on Jarrod Saltalamacchia's RBI double to left. Adeiny Hechavarria's sacrifice fly gave Eovaldi a two-run cushion.
After breezing through three innings, striking out five, Eovaldi surrendered two runs in the fourth. A one-out walk to Gonzalez put the inning in motion. Troy Tulowitzki laced an RBI double to the gap in right-center.
Justin Morneau reached on an infield single on a little popup that landed perfectly on the grass beyond the reach of Eovaldi and in front of the infield dirt near shortstop. The hit put runners on the corners, and the Rockies tied it at 2 on Wilin Rosario's sacrifice fly to right.
In the ninth, Cishek made quick work, logging one strikeout in his clean frame.
"We're sick of losing all those close games," Cishek said. "I did not want to start us on a bad note."