"That makes it so much fun," Murphy said, hitting behind the four at the top of the order.
"A lot of the success I've had this year, a lot of it is thanks to them. Every one of those guys, what they do speaks for themselves. Having Josh and Milton, who are the two best hitters in the league right now, hitting in front of me, that's awesome."
Texas trailed 5-1 after six innings, but sent 10 men to the plate in a seven-run seventh, matching its biggest inning of the season. Relievers Jeff Fulchino and Jimmy Gobble faced seven Rangers in the inning without retiring a batter.
"We're the type of offense that perseveres," Murphy said. "We showed that tonight."
Murphy, who leads all AL rookies with 46 RBI and 77 hits, hit a home run onto the right-field grass on a 2-0 pitch from Gobble (0-2). The grand slam came after Josh Hamilton hit an RBI single and Bradley walked to load the bases.
"I felt good in that situation," Murphy said. "The offense came out a little bit flat tonight, as it did last night. We showed a lot of fight and did what we do.
"I was fortunate to get into a 2-0 count. Bases loaded and 2-0, I'm pretty much looking dead-red fastball and that's what I got, right where I wanted it."
Murphy then led off a three-run ninth inning with a home run off Brett Tomko for his first career multi-homer game.
Vicente Padilla (8-3) picked up the victory and is 6-1 in his past nine starts, although he allowed five runs, four earned, on seven hits in six innings.
The Royals, who also squandered a four-run lead in a loss to Texas the previous night, have lost 19 of 23 games.
Royals starter Kyle Davies weaved his way in and out of trouble for six innings. The Rangers had at least one base runner every inning off Davies, who gave up six hits -- five of them singles -- and walked five, but allowed only one run.
"You've got to give Davies a little credit," Rangers manager Ron Washington said. "We had the bases loaded and he got out of it. We had runners at second and third and he got out of it. But these guys have a knack for scoring runs late. Our offense is what it is."
Davies pitched out of a jam in the second when he walked the bases loaded with one out, but Kinsler grounded into a double play. Davies was also aided by double plays in the fourth and fifth innings.
"I was hoping Fulchino would do a little bit better than he did," Royals manager Trey Hillman said. "You've got to throw strikes. Jimmy didn't throw well, obviously. Davies put us in a position to win the game, but obviously we still have a lot of trouble out of the bullpen."
Byrd led off the Rangers' half of the fourth with a double and scored on Gerald Laird's single for the only run Davies allowed.
"I rang my pitch count up pretty high early and we made some great defensive plays and got me out of some jams," Davies said. "A starting pitcher has to go as long as he can and be as effective as he can with the least amount of pitches."
Grudzielanek's double to right in the third inning gave the Royals a 2-0 lead. They added an unearned run in the fifth when Alex Gordon moved to third on Jose Guillen's single, then scampered home when Kinsler dropped the throw back into the infield.
- Murphy, Kinsler, Hamilton and Marlon Byrd each had three hits for Texas.
- Murphy also leads AL rookies in total bases (129) and multi-hit games (20).
- Young went 0-for-5 to snap his 23-game hitting streak, the longest in the majors this season.