Murphy had three hits and drove in two runs, Max Ramirez contributed the go-ahead RBI with a fifth-inning double, and the Rangers completed a four-game sweep with a 6-4 victory over the Kansas City Royals on Sunday.
"He did what he does, which is swing the bat and drive in some big runs," Washington said. "I've said all along that we're going to need Murph."
Murphy went 8 for 17 with four doubles during the series with the Royals while filling in for right fielder Nelson Cruz, who's on the 15-day disabled list with a strained left hamstring.
Cruz is expected to be activated this week, and he carried the Rangers early with seven homers that still lead the team.
But Murphy's recent hot streak has raised his average from .151 to .229, and manager Ron Washington won't park Murphy on the bench once Cruz returns.
Prior to the series, Murphy told himself to relax, that he was trying too hard.
"When I speed up my at-bats, my mechanics get out of whack a little bit and I don't see the ball as well," Murphy said. "That was my goal going into the series, and I feel like I did it successfully. We'll see what happens when (Cruz) gets back."
Doug Mathis (1-0) pitched two scoreless innings for the victory as the Rangers won for the 10th time in 13 games. Neftali Feliz got three outs for his third save in the series and ninth in 10 chances overall.
The Royals went scoreless over the final five innings against four Texas relievers.
Mike Aviles homered and had three hits for Kansas City, which completed a 3-8 trip.
"It was bad. It was real bad," Royals manager Trey Hillman said of his team's road woes. "If you had told me we would be 10 games under .500 at this time, I never would have believed it."
Kansas City's Mitch Maier had a two-run double in the second to open the scoring.
Texas answered with a four-run third against starter Luke Hochevar on Josh Hamilton's RBI ground-out, Vladimir Guerrero's sacrifice fly and Murphy's two-run double.
Hamilton went to second on Guerrero's fly ball, and after the game Hillman said Hamilton never tagged up. But none of Royals players on the field tried to appeal the play, and Hamilton remained at second.
Hamilton and Ian Kinsler later scored on Murphy's double.
"I had no clue," Kansas City first baseman Billy Butler said. "I didn't see it. Obviously I'm embarrassed about it now. I was watching the play in front of me. I didn't pick up on it. That's my priority. That's on me."
Hochevar, weak from an illness over the last couple of days, was gone after 2 2-3 innings and 71 pitches. He allowed four runs and three hits.
Aviles' leadoff homer and Yuniesky Betancourt's RBI double in the fourth pulled Kansas City even at 4.
Rangers starter Scott Feldman lasted only four innings, giving up four runs and six hits while throwing 100 pitches.
Texas took a 5-4 lead in the fifth on Ramirez's two-out RBI double off Brad Thompson (0-2).
Thompson retired the first two batters in the fifth before Murphy and Justin Smoak singled, and Ramirez drove in Murphy with a hit to right-center.
Michael Young's RBI single off Robinson Tejeda in the eighth extended Texas' lead to 6-4.
The Rangers have their first off day on Monday after playing 20 straight games, but Washington would rather keep riding the current hot streak.
"It seemed when we started playing baseball every day, things began to fall into place," Washington said.
NOTES: Cruz will play for Triple-A Oklahoma City on Tuesday and Wednesday nights on a rehab assignment. ... Washington said LHP Derek Holland will get his first start of the season Wednesday in place of LHP Matt Harrison. Washington said there is no firm date for roster moves that would recall Holland from Oklahoma City and send Harrison to the 15-day DL with left biceps tendinitis. Holland was already with the Rangers before Sunday's game for a bullpen session with pitching coach Mike Maddux. ... Several hitters from both teams used pink bats, batting gloves and wrist bands to mark Major League Baseball's "Go to Bat Against Breast Cancer" campaign.