"I hate pitching in this ballpark against any lineup. It's probably my worst ballpark in the league to pitch in," said Meche, who had an 8.10 ERA his previous eight starts in Texas. "I just tried to forget about it tonight. ... It was also good to get an early four-run lead."
Teahan led off the second with his homer and Coco Crisp hit a three-run shot later in the inning off Matt Harrison (0-2). The Royals led 12-0 before Hank Blalock and Marlon Byrd hit back-to-back homers in the eighth.
The Rangers were coming off a 19-6 victory over Baltimore on Wednesday night, a game in which they had 19 hits while Ian Kinsler went 6-for-6 with a cycle.
The Rangers managed only six singles off Meche (1-0), who struck out six before being pulled after consecutive hits to start the seventh. The right-hander, 11-3 with a 3.09 ERA in his final 21 starts last season, has a 2.25 ERA in three starts this season.
"He was throwing everything for strikes, the changeup, curveball, fastball," Michael Young said. "he was moving in and out, and kept us off balance."
Jamey Wright gave up a one-out single to No. 9 hitter Elvis Andrus to load the bases before he struck out Kinsler. It was then Young's turn to bat, but manager Ron Washington instead inserted Omar Vizquel.
Young knew Vizquel was going to replace him at third base the following inning, but Young figured he'd bat until he was told otherwise just before going to the on-deck circle.
"I'm not going to question it," said Young, the five-time All-Star. "It's Wash's call."
But Murphy batted in Hamilton's spot leading off an inning, instead of with the bases loaded like Vizquel did for Young.
"When you look at it the way you're looking at it, I have to take the blame if you think it was the wrong thing," Washington said. "But right there, I told Vizquel that he is going in before we even got started [that inning], and told him he was going to get the at-bat."
Vizquel hit an inning-ending foul pop on the first pitch.
"If we can slug it the way we did today, that's good to see," Hillman said.
One of the singles off Meche was Kinsler's bunt leading off the third. Including his walk in the first, Kinsler reached base nine consecutive plate appearances before a deep flyout to center in the fifth.
Callaspo made a pair of nifty defensive plays in the sixth.
With a runner a first, he made a diving stop of Hamilton's grounder up the middle, then was face down on the dirt when he flipped the ball over his shoulder to shortstop Mike Aviles covering second base for the forceout. Callaspo then had to make a full extension over his head to stab Byrd's liner to end the inning.
Kansas City started the seventh against reliever Willie Eyre with consecutive doubles by Teahen, Jacobs and John Buck. After Callaspo's flyout, Willie Bloomquist greeted reliever Josh Rupe with an RBI double to make it 9-0. Jacobs added his third homer, a three-run shot, in the eighth.
Jarrod Saltalamacchia led off the ninth with his second homer, coming after a 2-for-26 slide in which he struck out 12 times. He stuck out his first three at-bats Friday.
Texas has multiple homers in all seven home games this season, matching its longest such streak in Rangers Ballpark history. ... Kinsler is sending a bat he used during in his cycle game to baseball's Hall of Fame, but will keep the jersey he wore. "It will be real cool to have it on my wall," Kinsler said. ... Ryozo Kato, commissioner of Nippon Professional Baseball in Japan, will visit Rangers Ballpark on Monday. ... Jacobs had to step out of the box during his at-bat in the seventh when some fireworks -- part of the postgame show -- prematurely went off.