But Cook (15-8), who had lost his previous two starts and had another one postponed due to back stiffness, can delight in the gifts he received from his teammates.
Cook, who gave up seven hits and two runs in five innings, was the beneficiary of no fewer than three stellar defensive plays -- two by second baseman Clint Barmes.
Ian Stewart's three-run homer in the fourth off Odalis Perez (5-9) made a winner of Cook, and Brad Hawpe's solo shot and Seth Smith's three-run homer in the eighth let Cook relax.
"It's a long season and a long career," Cook said. "You've just got to kind of ride it out, take the good with the bad.
"Sometimes, the bad ones are better than they seem, and the good ones aren't as good as they seem."
The Rockies, meanwhile, are hoping the season isn't as bleak as it seems.
They're 12 games below .500 with 36 to play, but can brighten their outlook with a three-game road series against the Dodgers -- one of two teams ahead of them in the National League West -- starting on Tuesday. They're 2-4 at Dodger Stadium this season.
"We'll enjoy [Monday] off, but we'll look forward to playing the Dodgers," Rockies manager Clint Hurdle said. "They're on top of us. We've got a chance to do something good."
Cook became the sixth pitcher in Rockies history to win 15 games, and is two behind the franchise record, shared by Kevin Ritz (1996), Pedro Astacio (1999) and Jeff Francis (2007).
The first good omen came with one out and one on in the first.
Lastings Milledge hit a hard bounder to Cook, who fired to second base. Cook had what he called "a bad changeup grip," and the ball sailed past shortstop Troy Tulowitzki, who was covering the bag. But Barmes alertly backed up the play and gunned a throw to first in time to retire Milledge. A groundout later, Cook was out of the inning.
Then, with the Nationals up, 1-0, with runners at second and third and one out in the second, Barmes charged to field Wil Nieves' chopper and threw home to retire Ryan Langerhans.
First baseman Garrett Atkins dove to stop a hard-hit Perez ball from escaping down the line in the fifth. The play helped hold the Nationals to one run in the inning, as Cook coaxed a flyout by Langerhans with the bases loaded to end the threat.
Cook, who struck out four and walked three, said his less-than-sharp performance was not because of his back, but rather a mechanical flaw. He'll work with pitching coach Bob Apodaca to correct it before his next start.
"I was kind of falling on the outside of my [left] foot a little bit, kind of rolling toward first base," Cook said. "Everything felt fine except for that."
The Rockies continued with the defensive gems after Cook left, sending the Nationals to their 10th straight loss -- the franchise's longest skid since moving to Washington in 2005.
Reliever Matt Herges gave up two hits to lead off the sixth, but Manuel Corpas replaced him. The infield turned a double play on the speedy Emilio Bonifacio to end the threat.
With Corpas still on the mound in the seventh, Matt Holliday went near the wall to grab a Milledge liner, and he slid to catch an Aaron Boone drive.
"They had things going in every inning," Hurdle said. "It's not like they weren't trying. They were on base. They couldn't get a big click of the bat. We made some plays ... 7-2, it was a lot closer ballgame than that."