"There's still some guys still playing that I grew up watching," Hochevar said. "To be able to pitch against them is a dream come true.
"You have to think of them just as hitters in there," he said. "Todd Helton, he's a future Hall of Famer. If that's going through my head, I'm in trouble."
The Royals swept the series and improved the majors' best interleague record to 12-3. Kansas City has won 10 of 11, all against National League teams.
Hochevar (5-5), born in Colorado and the No. 1 overall pick in the 2006 draft, held the Rockies to two runs and seven hits.
Hochevar did run into trouble in the second, when the Rockies bunched together four hits but scored only one run. Chris Iannetta's two-out double scored Garrett Atkins, who led off the inning with a single.
"When you get in that type of situation, it is either fight or fly," Hochevar said. "I just took the ball and thought to myself, 'I'm just going to go right after them. I'm going to keep the ball down, be aggressive and whatever happens, happens.' That was the turning point. That was good for me.
"That's usually my approach after a rough outing or I hit a skid, go out and compete like a mad man and keep the ball down," he said.
After a 12-game losing streak in May, the Royals' recent surge has allowed them to climb past Cleveland and out of last place in the AL Central.
"That's a step, no doubt," Royals manager Trey Hillman said. "Sometimes, you'd like to take large giant steps, but we dug ourselves such a big hole that we're going to have to get back in it with baby steps."
After Hochevar gave up a two-out double to Helton in the third, Hochevar retired the next 10 batters before Brad Hawpe homered to leadoff the seventh.
Joakim Soria worked a perfect ninth for his 21st save in 22 opportunities.
"We're always trying to add on," Gload said. "It's always good to get one or two RBI. Two is always better. He pretty much always throws the sinker. You really can't look for anything else."
Cook was bidding to join Arizona's Brandon Webb for the most wins in the NL. Cook lasted 5 1/3 innings and allowed three earned runs and eight hits.
"I knew they would be well prepared for me," Cook said. "I had (Royals pitching coach) Bob McClure as a pitching coach for about 4½ years, so I knew they'd be ready for everything I threw at them.
"I made pretty good pitches except for a couple in the sixth inning and then Gload hit a pretty good pitch and he was just able to keep it fair and rap it down the first base line. I left it all out there and unfortunately I didn't pitch as well as I should have."
The Royals took advantage of errors by Atkins at third base and Omar Quintanilla at shortstop to score twice in the third. Gload led off the inning with a double, David DeJesus hit an RBI single and Alex Gordon had a sacrifice fly.
"If we played better defense behind him, the whole dynamic of the game has a chance to change," Rockies manager Clint Hurdle said. "I thought it was a good outing for him. It's not the right results. Gload got him in a big way. He kept us in the game and probably deserves a better line than the one he finished with."
Buck threw out Ryan Spilborghs trying to steal second in the eighth. The Royals catcher had been 0-for-23 in throwing out runners this season.
- Plate umpire Angel Campos issued a warning to both benches before the first pitch after Royals RHP Ramon Ramirez threw two pitches behind Rockies C Yorvit Torrealba in the ninth inning Tuesday.
- Royals 2B Mark Grudzielanek sat out his fourth straight game with soreness in his lower back.
- Rockies LF Matt Holliday went 0-for-3, ending his season-high 11-game hitting streak.
- DeJesus had two singles and extended his hitting streak to 11 games.