Shields, who can become a free agent after this season, needed only 10 pitches to get three quick groundouts.
"For me, it's the ups and downs, it's what you've got to get used to as a starter," Shields said. "You heat up and cool down, heat up and cool down. We don't practice that."
"The pitches don't really matter as much. I went to the bullpen and threw an extra 20 pitches to get my pitch count up. It's all about pacing yourself," he said.
Shields said in his next outing he would probably throw 45 pitches and three innings.
Moustakas, who batted only .233 with 42 RBIs last year, hit a two-run double in the second inning off Alexi Ogando and a RBI single off Jose Contreras in the third.
"It's just spring and we're working on some stuff to iron some things out," Moustakas said. "The results are second right now in spring training, although it's always good to have them. It's a little bit of a confidence boost. The work is translating right now from out early in the mornings to the games."
The Royals got 16 hits. Billy Butler went 3 for 3 and Alex Gordon and Norichika Aoki each singled and doubled.
Aoki also walked and reached on shortstop Elvis Andrus' throwing error.
"That's who Aoki is," Royals manager Ned Yost said. "He's a real consistent performer."
The Rangers managed just six singles off seven Kansas City pitchers.
Rangers: Ogando, who was on the disabled list three times last season, gave up two runs on four hits in two innings. He threw 19 strikes in 34 pitches, striking out one and walking none.
"I got behind the count to a lot of the hitters," Ogando said through a translator. "That's something I'll take into the next outing. I'm happy with this being the first outing. I'm healthy and that's what is most important."
Royals: Left-hander Jason Vargas, a free agent signed to a four-year $32 million contract in November, will make his first start Saturday against San Diego.
Rangers: Right-hander Nick Tepesch, who had been set back with back tightness, reported no issues after throwing batting practice. He is scheduled to pitch two innings Monday. ... Second baseman Jurickson Profar, who has shoulder tendinitis, continues to progress in his throwing program.
Royals: Reliever Louis Coleman is being held out of early exhibition games after bruising a finger in fielding practice. He is throwing bullpens, but the club is being cautious.
Royals shortstop Alcides Escobar left to be with wife Francys, who is expecting the couple's first child on Saturday. Rookie Christian Colon, the fourth overall pick in the 2010 draft, replaced Escobar at shortstop and contributed a two-run single.
The 42-year-old Contreras, a non-roster invitee to camp, gave up four runs on six hits in the third inning. Contreras missed most of the 2011-12 seasons after a pair of elbow surgeries, and pitched five innings last year for Pittsburgh. The Rangers have had just three players 42 or older appear in a regular-season game — Nolan Ryan, Charlie Hough and Omar Vizquel.