There were other offensive sparks, of course. Mark Grudzielanek returned from five games off with a back ailment and banged three doubles and a single. Mark Teahen ripped a two-run triple in the eighth inning to seal the win and finished with three RBIs.
Royals starter Brett Tomko was knocked out in the fourth inning after surrendering five runs, but the bullpen was able to contain the Rangers.
"I'm just fighting it right now," Tomko said. "My secondary pitches are just garbage; they're just not working."
Four relievers were brought into the fray -- Ron Mahay, Jimmy Gobble, Ramon Ramirez and Joakim Soria -- and they combined for 5 2/3 scoreless innings.
Mahay, a long-time Ranger, was awarded the victory -- to his surprise.
"I didn't know," Mahay said. "It is good, obviously, when you come back here after being with them for the last five years. It's always a good feeling."
He went 2 1/3 innings, getting his last out on Grudzielanek's superb catch as he raced into right field for Michael Young's popup.
Guillen collected his five RBIs in his first three at-bats.
"He swung the bat very well tonight, and the more he does that the better off we're going to be," Royals manager Trey Hillman said.
Actually, Guillen got a bit lucky on the first RBI. Batting in the first inning with runners at second and third base, Guillen hit a bouncer to Texas third baseman Ramon Vazquez. His throw home seemed in time to retire Grudzielanek, but home-plate umpire Bill Welke ruled him safe. It was scored a fielder's choice and an RBI.
"He hung that pitch, and I got too anxious, but it worked out all right for us," Guillen said.
It was a night of hanging pitches for Rangers starter Jason Jennings, who finally retired in the third inning because of an irritated ulnar nerve in his right arm.
With the bases loaded in the second inning, Guillen lashed a solid single to left field for two runs and a 5-0 Royals lead. He battled Jennings to a 3-2 count on that at-bat.
"I was lucky right there -- I got the hanging curve," Guillen said. "Sometimes, as a hitter, you look for those mistakes. Especially when you're struggling, you're hoping the guy keeps throwing the ball like that and hanging the breaking pitch."
After Alex Gordon singled to open the fourth, Guillen lofted a high 400-foot home run just fair into left field against right-handed reliever Scott Feldman. The ball was reported to be the first to land in the lower suite level that hangs over the bleachers at Rangers Ballpark.
Yep, another hanging breaking pitch.
"I was pretty much sitting on it," Guillen said.
The five RBIs matched Guillen's career best, achieved six times previously. The last time came last Aug. 19 against the White Sox when he was swinging for the Mariners.
The outburst gave Guillen a club-high 15 RBIs. He was 2-for-4 and also walked. His average eased up to .190.
Even though the Royals held a four-run lead going into the ninth, Hillman opted to bring in his closer, Soria, rather than hold him for a tighter game.
Hillman was thinking back -- to a three-game sweep dealt out by the Indians last week -- and ahead -- to a three-game visit to the Tribe this week.
"I thought Texas was a pretty good-hitting team," Hillman said. "[It was the] first game of a six-game road trip. [We were] playing the last three in our division against a team that just got finished spanking us, and I wanted to make sure we nailed this first one down."
Soria got in a bit of a jam on a rare Grudzielanek error and his own first walk of the season. But he worked out of the trouble and still has not allowed a run all season.