The Rangers scratched Darvish, the Japanese star who won 16 games as a rookie, with what the club termed a "very minor" neck strain.
"I think today was obviously Darvish not being able to start," Lowe said. "I was scheduled to pitch two innings. You never like to see anybody get injured, but it actually worked out in my favor to get an extra inning out of it."
Lowe, who signed a minor league contract with the Rangers on March 6, gave up three singles, walked one and struck out three against a Royals' club that entered the game with a spring training-best .335 batting average. He threw 28 strikes in 47 pitches in his second outing.
"It was a lot better, a lot better breaking ball, command of the sinker was a lot better," Lowe said. "We added a cutter today. You're starting to get your legs underneath you a little bit where you feel like you can compete no matter how long you're out there. All in all, it was a good day."
Lowe, who turns 40 on June 1, has been a closer and a starter. Last season he went 8-10 with a 5.52 ERA in 21 starts with Cleveland and 1-1 with a 3.04 ERA and one save in 17 relief appearances with the New York Yankees. The Rangers still have an opening for a fifth starter.
"I think you're asking a little much," Lowe said. "I said all along when I talked to (Rangers general manager) Jon Daniels I just wanted an opportunity to compete for the job or any job. There was never any talk of anything. And I was fine with competition, try to go out and earn your way on the team.
"Let's be honest, look around. There's 34 pitchers still in camp or whatever it is. I'm out here to fight and claw to grab onto any role that's possible," he said. "That's all I really care about. It doesn't matter if it's a half inning, one inning, five innings."
Darvish said in a statement that the move is "just precautionary" and that he would have made the start in the regular season.
The Japanese ace said he felt what he called a very mild strain in his neck during a workout Sunday that caused the stiffness.
"It's not a setback at all," Rangers manager Ron Washington said. "In the season, he would have pitched, and you wouldn't have known anything about it. But it doesn't make any sense if he's feeling something down here."
In his first three appearances this spring for the Rangers, Darvish has allowed only one run with 10 strikeouts in 8 2/3 innings.
Kinsler homered off Ervin Santana.
Santana, who the Royals acquired in an off-season trade with the Los Angeles Angels, allowed six runs on 10 hits in four innings. Santana had a 14.46 ERA in three starts last season against the Rangers.
"Everything was a little bit up," Santana said. "That was the problem today. I was leaving the pitches up a little bit and behind in the count, too. It happens. I'm human. Nobody's perfect. Better down here (Arizona) than up there."
Brandon Wood, who was reassigned to minor league camp after the game, hit a two-run two-out ninth double for the only Kansas City runs.
The Royals optioned LHPs Will Smith and Everett Teaford and RHP Nate Adcock to their Triple-A Omaha club. They reassigned non-roster invitees RHP Yorando Ventura, Brian Sanches, Blaine Boyer and Michael Mariot, C Adam Moore, OF Willy Taveras and IFs Christian Colon, Anthony Seratelli and Wood to minor-league camp. .LHP Derek Holland returned to the Rangers' camp after pitching for the USA in the World Baseball Classic and will throw in a minor-league game Tuesday. .RHP James Shields did not pitch Sunday against the White Sox, who he will likely face in the April 1 Royals' opener at Chicago, but instead worked in a minor league game. He allowed two hits in six scoreless innings, walked one and struck out eight. He threw 54 strikes in 76 pitches. . SS Alcides Escobar returned to the Royals' lineup for the first time since March 10 after being setback by back spasms. .Lance Berkman played first base, the first time he was in the field for the Rangers after DHing in 12 games.