Colorado gained a half-game on the idle Padres, who now lead the Rockies in the National League West by four games. The Rockies sit three games below .500.
The pitchers wasted little time getting the ball to the plate, and they needed few pitches to get the jobs done.
Cook (7-9) threw 104 pitches in eight innings (3.25 per batter faced). Brewers starter Chris Capuano (10-7) needed only 93 pitches in eight innings (three per batter faced). Brian Fuentes needed seven pitches in the ninth to earn his 20th save of the year.
"I like to go out there and work quick," Cook said. "It's one of those nights where I actually had stuff working, which is a delightful change after my last couple starts."
Cook gave up two runs on four hits. He struck out four and walked three.
He said he felt hitters had started focusing in on his sinker in recent games, so he made a conscious effort to mix in his slider.
"That was a key to keeping them off my sinker a little bit better," he said. "I knew that I wanted to keep them off-balance. ... When I can get my slider over, it definitely opens more doors for me with my fastball."
Catcher Yorvit Torrealba said that was part of the plan.
"It worked out perfect," Torrealba said.
Cook induced 14 groundouts, and he was able to work out of a bases-loaded jam in the fifth inning with only one run scoring. Manager Clint Hurdle said that was a big one for Cook.
Hurdle added he considered sending Cook out to complete the game, and he would have done so if the Rockies were up by four runs. Cook said he could have gone all nine.
"We want to run with him [Fuentes] while he's hot," Hurdle said.
The Rockies had lost 11 of Cook's previous 12 starts. He was 1-6 during that stretch, although he had pitched fairly well in most of those games. The Rockies had scored two or fewer runs eight times during that stretch, and the bullpen had blown four leads. Cook had last won on June 27 against the Angels.
But Monday, the Rockies' offense gave Cook some support, particularly early in the game.
They scored two in the first with a double, a walk and two singles, and then hit the two homers in the third. Holliday has three homers in the last four games.
"It's a big difference just to go out there and know you have a two-run lead," Cook said. "It let me relax a little more and keep my game plan and worry about pitching."
Said Atkins: "It gives the pitcher a little bit more comfort knowing that he can make a mistake, and if it happens, it's not the end of the world, like if it's 0-0 in the fifth."
Just a few hours after the 2 p.m. MT non-waiver trade deadline, the Rockies took the field with pretty much the same team they have had for the entire season -- something that hasn't happened in recent years.
"It's nice this year," Cook said. "Everybody knows they've been doing their job. We are right in the middle of it, and we're still relaxed and having fun playing baseball."
Todd Helton, who had an RBI single in the first agreed, saying it was good that there was no remaking the team around the deadline.
Several of the Rockies' division rivals made more moves on deadline day.
The Rockies made only one trade, exchanging Ryan Shealy and Scott Dohmann for Kansas City pitchers Jeremy Affeldt and Denny Bautista.
The Rockies didn't seem too bothered by the moves made by their NL West rivals.
"We feel like we can match up with anybody, no matter who they went out and got," Cook said. "Other teams made trades they felt they had to make. We didn't feel like we needed to make any. I don't want to say the wrong word here, but that just gives our guys more confidence from the coaching staff and management that we have what it takes here."
The NL West race is tight, with the last-place Dodgers just five games out.
Hurdle said he would worry about his team and not the dealings of division rivals.
"We're taking care of our own backyard," he said.
This was the 1,000th win in the Rockies' 14-year history. The Marlins, whose first season was also 1993, picked up their 1,000th win on July 7.