With the score tied at 5, the Rockies sent 10 batters to the plate in the eighth to break the game open. Ryan Spilborghs began the inning with an infield single off Mateo (0-1) and Jose Lopez doubled, breaking out of an 0-for-18 skid.
After Jose Morales and pinch-hitter Ty Wiggington each fanned on wicked sliders by Mateo, Fowler lashed Mateo's 2-2 offering to right center to give the Rockies the lead. Jonathan Herrera and Carlos Gonzalez, who had four hits on the day, followed with RBI singles.
"He tried to get ahead of me with the fastball but his slider is his go-to pitch," Fowler said. "I swung through one but I just had to stay patient. He threw another and I just wanted to put the barrel on it and do something with it."
He did enough to help Colorado bounce back from a rare early season loss the day before, 8-3 to the Cubs.
"We have a bunch of different weapons and we can hurt you a bunch of different ways," Fowler said. "I'm just happy it was my turn. And it was important to come off [Saturday's loss] like we did. It shows the character of the team. We had lost a couple of close games but that was our first real blowout. We bounced back nicely."
Chicago manager Mike Quade said Fowler helped make the difference by getting hold of a good pitch.
"The one thing that Matty couldn't do, because he made some good pitches, was he couldn't finish somebody with a slider down and out of the strike zone, and that's what he needed to do," Quade said. "It's a quality slider but just couldn't get it down enough."
Neither starter figured in the decision and both Chicago's Ryan Dempster and Colorado's Alan Johnson, who was making his major league debut, did not fare well in the cool, blustery conditions at Coors Field.
Dempster gave up five runs on seven hits in five innings while Johnson was touched for five runs on six hits in four innings.
"I give Alan Johnson credit. He battled," Colorado manager Jim Tracy said. "He got himself into some pickles due to the fact he was trying to pitch out of hitters' counts. They dinged him here. They dinged him there."
But Chicago didn't touch Colorado's four relievers, who pitched five scoreless innings.
Rafael Betancourt (1-0), the fourth of five Rockies pitchers, entered in the eighth and picked up the win with two-thirds innings of hitless relief.
"They've been absolutely tremendous, to take the game over from the fifth inning on and put zeroes up there," Tracy said. "You can't say enough."
The Rockies overcame the loss of a key part of their offense when Seth Smith was lifted in the top of the fifth inning because of tightness in his left groin. He hit a two-run homer and doubled and scored before being replaced by Spilborghs. His playing status was day to day.
The Rockies got to Dempster for four runs in the first inning but fell behind 5-4 in the fourth after Geovany Soto walked, was sacrificed to second and then scored on Starlin Castro's two-out double off Johnson.
The game was tied again in the bottom of the fourth when Smith scored from third on a groundout by Jose Morales after doubling to start the inning.
Soto's RBI single in the second pulled Chicago to 4-2. The Cubs evened the score 4-all when Aramis Ramirez delivered a run-scoring single and Darwin Barney came home on second baseman Herrera's errant throw to first while trying to complete a double play.
Gonzalez, whose four hits in a game matched a career high, started the Rockies' first-inng rally with a run-scoring double and Smith followed an RBI single by Todd Helton with a home run that sailed into the bleachers behind the center field fence.
Castro, who singled to start the game and finished with three hits, scored on a double play grounder in the first.
Dempster fanned Johnson in the fourth for his fourth strikeout of the game, pushing his career total to 1,600. ... A year ago to the day, Ubaldo Jimenez threw the first no-hitter in Rockies' history against the Atlanta Braves at Turner Field. Jimenez (right thumb) is set to make his second start this season when he returns from the disabled list on Tuesday against San Francisco. ... In going 4 for 5 on Saturday, Castro at 21 years, 24 days old is the youngest player in the majors. He became the first Cubs player to get four hits, including a home run, in a game, before his 22nd birthday since Ron Santo did it twice in 1961.