MIAMI -- Some like it hot. Smokin' and steamin' Jose Guillen certainly did on Sunday, as the temperature rose into the 90s at Dolphin Stadium.

Guillen blasted a home run, a double and finished with four RBIs as the Royals knocked off the Florida Marlins, 9-3. He extended his hitting streak to 10 games -- in which he's batted an even .500, going 19-for-38, with two homers, eight doubles and 15 RBIs.

"I'm just working hard and I keep getting better every day. I'm putting in some hard work, and it's just paid off in the right way," Guillen said.

"We came into some great weather and I'm helping this team to win, and that's why they got me here. I know there was a lot of concern early in the season, but we've been turning it around the right way."

The Royals certainly have, as well, winning for the sixth time in seven games.

"We're in the right direction now -- we're winning and that's the important thing," Guillen said.

Right-hander Zack Greinke worked six innings for the victory, boosting his record to 5-1. He also rapped two hits, although neither figured in the scoring.

After playing most of the spring in chilly weather, the Royals loosened up in warm South Florida and took the Interleague series, two games to one.

Guillen fired things up in the first inning. David DeJesus and Alex Gordon were at the corners after singles and then scored when Guillen planted a drive onto the left-field wall.

Guillen was up again in the third when two more runs scored, but this time it was primarily the doing of Marlins third baseman Jorge Cantu. He fielded Guillen's slow bouncer and flung the baseball low past first base for a two-run error.

On right-hander Burke Badenhop's next pitch, Mark Teahen sent a drive banging around the stadium clock mounted high on the left-field fence. The clock tolled two more runs and a 6-0 lead for the Royals and Teahen's first homer in 141 at-bats, since April 3 at Detroit.

That's right -- just two homers for Teahen so far.

Guillen hit his fifth homer and reached 30 RBIs in the seventh when he belted a 3-1 pitch from reliever Logan Kensing over the left-field wall. That made Guillen 6-for-12 with eight RBIs in this series and he boosted his average to .245.

Greinke joined in the hitting fun, pounding a double deep into the left-center gap in the second inning. That was his second Major League hit; he had homered against Arizona in 2005.

The Marlins' third wasn't quite so much fun, because Greinke faced the bases loaded with no outs. He wriggled out with just one run in, but Mike Jacobs led off the next inning with his 11th home run.

Greinke got another hit, an infield single, in the sixth inning. That meant he was the first Royals pitcher with two hits in a game since Steve Busby on Sept. 20, 1972, at California. Busby had three hits in that game, which was so long ago that it was in the pre-DH era.

Greinke, whose home run was the last one hit by a Kansas City pitcher, knew about the Busby business before the game ended.

"My dad texted me that," Greinke said. "Yeah, I'm getting all the records. I got the home run, now the two-hit game."

In the bottom half of the sixth, Hanley Ramirez's single and Dan Uggla's booming double cut the Royals' lead to 6-3. Greinke caught a break when, on Luis Gonzalez's single to left, Uggla was thrown out at the plate by Guillen.

Guillen, on this hot day, seemed to be capable of anything.

"Great job, great series," manager Trey Hillman said. "He takes the pressure off everybody else when he's hitting like that. Great throw from the outfield. He's playing through some stiffness in the hip. Never wants to come out."

That ended the inning -- and Greinke's outing. The Royals were watching him closely on the hot afternoon, mindful that Brian Bannister had run out of gas quickly in Saturday night's loss.

After Guillen belted his home run, Greinke's fifth victory was in hand and left-hander Jimmy Gobble took over on the mound and worked two innings. Yasuhiko Yabuta finished up.

When the Royals got their 14th hit, it was Matt Tupman's single in the ninth inning -- his Major League debut.

"That's special -- his teammates were excited for him," Hillman said. "One at-bat, one hit and he's hitting 1.000."

Guillen sizzled in the heat and Greinke, from Orlando, Fla., felt right at home.

"Today was a little hot, but I don't mind -- I'm from this area, Greinke said. "As long as you're not out there too long, you're fine. It wasn't too bad. I like the heat."

Yep, some like it hot.