Cook pitched seven innings, dominating the Angels hitters and giving up only one run on three hits and two walks.
The lone run off Cook came in the fourth inning, when first baseman Kendry Morales hit a solo home run to short right field.
"It was quite a statement from Aaron," Rockies manager Jim Tracy said. "I think there is more to come from him, though, as he moves on through the course of his career.
"He was sensational tonight -- and as heavy a sinker I have seen since we started the season. It was very difficult for anyone to get a good swing."
Before the game, Tracy alluded to the fact that Cook's success hinges on his ability to get ground-ball outs, and if he can do that early, he has a great chance to get the victory.
Case in point, in the first inning, Angels third baseman Chone Figgins and designated hitter Vladimir Guerrero both recorded groundouts.
Through Cook's seven innings, he recorded a total of 13 ground-ball outs.
"The win really meant a lot to me," Cook said. "The organization has shown a lot of confidence in me over the years and has supported me through some ups and downs, and it is something I am going to look back and enjoy, just not for that long."
The Rockies helped Cook's case early and often, when in the second inning they scored three runs on three hits, including an RBI single from third baseman Ian Stewart and a two-run single by designated hitter Seth Smith.
In the fifth inning, Dexter Fowler singled and Todd Helton walked before Brad Hawpe smashed a three-run home run to straightaway center field.
Angels starter Matt Palmer, putting his perfect 6-0 record on the line, didn't last long, pitching 4 2/3 innings and giving up six runs on seven hits and five walks, for his first loss.
Angel relievers didn't do much better, giving up five runs in 4 1/3 innings.
"The way they played tonight, we saw firsthand the way they've been playing the last few weeks," Angels manager Mike Scioscia said. "Their hitters were very disciplined. They made Matt get in the zone, and when he did, they were ready for him."
The Rockies were also helped by six wild pitches, which tied an Angel club record.
Five Colorado players had two hits, including Hawpe, who celebrated his 30th birthday, and Smith, who also set a new career high with four RBIs in one game.
"Smith was absolutely by no stretch of the imagination any kind of a disappoint for us offensively the way he swung the bat," Tracy said. "Hawpe also hit a big home run that really opened the game up for us."
Righty Juan Rincon pitched a scoreless eighth inning on 22 pitches in his first appearance with the Rockies this season. Reliever Matt Daley also pitched a perfect ninth.
Yet, after the game, the talk in the clubhouse was still on Cook and his record win.
"We had a lot of good solid hits tonight," Hawpe said. "Yet, ultimately, what it comes down to is quality pitching, and that is what we got out of Cook."