"For us to go out there and win a one-run game was huge," said Cook (2-1), who gave up four hits and two runs -- one unearned on his sixth-inning throwing error -- and struck out three.
"It's like going out there as a starting pitcher and you don't get your first win for a while. Then you get your first one and take off on a roll."
Cook earned his 54th Rockies victory and moved ahead of Pedro Astacio (1997-2001) for second on the club's career list. Jason Jennings (2001-06) is the current leader with 58.
"We felt confident," Rockies manager Clint Hurdle said. "We felt we'd win one before this. It's taken this long to do it, but we're able to do it. That's a big step."
While the Rockies (12-18) are taking care of the to-do list, they need to have some sustained success. Sunday's victory ended a losing streak at three games, kept the Marlins from sweeping the three-game series and improved them to 2-3 in an eight-game homestand that continues with Tuesday night's opener of three against the Houston Astros.
The Rockies showed some elements on Sunday that could lead to a roll.
Cook forced 10 ground-ball outs. Even though he was less efficient in his last three innings than his first three, he never lost control of the game. Relievers Matt Daley, Alan Embree and Huston Street (four saves) kept the Marlins quiet.
Also Helton made three dazzling defensive plays at first base, and left fielder Seth Smith (2-for-3, a double and a walk) made two standout catches -- one when he leaped at the wall for Alfredo Amezaga's drive in the seventh.
Troy Tulowitzki homered in the first inning but left in the ninth after feeling a slight strain in his left quadriceps, an area where he suffered a torn tendon and missed 47 games last year. Tulowitzki's replacement, Clint Barmes, made a key defensive play, when he fielded a one-out grounder from Cody Ross and caught pinch-runner Cameron Maybin in a rundown between second and third.
The offense was still incomplete. The Rockies left nine on base, went 1-for-9 with runners in scoring position and struggled with Marlins starter Chris Volstad (2-2), who gave up three runs (two earned) on seven hits in six innings but forced 11 ground-ball outs.
The first inning was the Rockies' best.
Tulowitzki homered for the fifth time this season and second time in as many games. Helton drove a triple to right that caromed off the scoreboard and away from Marlins right fielder Jeremy Hermida.
It was the first triple for Helton, who is 35 and has dealt with years of back problems, since he collected two against the Astros on June 5, 2007, at Coors Field.
"It had to bounce a long way for me to get to third," said Helton, whose double in the fifth drove in Cook, who had reached via error.