The win also completed a four-game sweep for the Rangers.
"It's really hard to sweep any team in four games," second baseman Ian Kinsler said. "It's one of the toughest things to do but we really battled out there and the bullpen did an unbelievable job."
The Rangers have also won 13 of their last 18 games and hold a one-game lead over the Athletics in the American League West. The two teams face off in a three-game series on Tuesday as the Rangers have a day off to bask in their sweep of the Royals.
"Today was a nice way to finish off the weekend," Rangers manager Ron Washington said. "This was a team effort from Thursday to Sunday. We got it done in every way we needed to get it done. The guys did a great job."
Murphy had a two-run double in the Rangers' four-run third inning and a single that put him on base to score the go-ahead run in the fifth. Murphy was 8-for-17 with three runs, four doubles and four RBIs in the series, raising his average back up to .229.
"I knew going into the series all I needed to do was relax and slow it down," Murphy said. "When I try to speed things up, my mechanics get out of whack and I don't see the ball. I just tried to slow it down and I was successful."
Murphy now has 12 RBIs in his last 17 games and 13 in 70 at-bats on the season. That comes out to an RBI for every 5.38 at-bats. That would put him in the top 15 in the American League if he wasn't a fourth outfielder and had enough at-bats to qualify.
But between Murphy and Nelson Cruz, the Rangers have 26 RBIs in 32 games from their right fielders. Murphy is now hitting .318 with runners in scoring position.
"I like those hits when there are men on base," Murphy said. "It feels good when I'm driving in runs. That's the biggest thing I can contribute to this team."
Murphy also had a little luck going for him when he came up to bat in the second inning with Kinsler on first and none out. Murphy took a hack at a 2-2 curve ball and two things happened. He clipped catcher Jason Kendall's glove with his bat and he hit a roller in front of the plate.
Everybody stopped, thinking catcher's interference would be called. Murphy ran to first without a play being made on him. Normally catcher's interference is ruled an error, but not if a player gets an actual hit on the play. Since nobody made a play on Murphy, he was actually given a hit.
"I've never even heard of that rule," Murphy said.
It was just part of a great day and a big series for him. But the biggest hit came in the third. Batting with two on and two out, he ripped a double into the right-center-field alley to break a 2-2 tie.
It was 4-4 in the fifth when Murphy singled with two out off Royals reliever Brad Thompson. He ended up scoring on a single by Justin Smoak and Max Ramirez's double.
"He did today what Murph always does," Washington said. "He swung the bat and drove in some runs. I'm glad he's swinging the bat because I've said all along we're going to need him."
They did this weekend.