Shoemaker, who Angels manager Mike Scioscia said is "like Nolan Ryan" when he pitches, dipped into the eighth inning for his second straight start.
"He may be 10 miles an hour short [of Ryan], but he goes out with that attitude, with that makeup," Scioscia said. "He goes out with the idea of a gunslinger. 'I'm going to make my pitches and I'm very, very comfortable in what I need to do out there on the mound.'
"All the clichés you want to say. Trusting your stuff, pitching to contact; I could line them all up. Matty lives it, and it's great to see."
The win, completing the Angels' first three-game home sweep of Texas since April 2007, was the third in a row for the Halos (41-33), while the loss marked the fifth consecutive defeat for the Rangers (35-40). Coupled with Oakland's loss, the win pulled the Angels within five games of the American League West leaders.
In four of his first six starts, Shoemaker (5-1) has faced All-Stars, including two Cy Young Award winners. The 27-year-old had already matched up with Cliff Lee, David Price, James Shields and Chris Sale, with the Angels winning three of those four games.
Now add Sunday's victory over Darvish.
"It doesn't really come into play, but the aftermath is pretty cool," Shoemaker said. "Those guys have done a lot in this game, and hopefully I can be in their shoes one day later down the road. It's definitely something you want to savor."
Darvish (7-4) struggled early on against the Angels' lineup, surrendering five runs (four earned) in the first 3 2/3 innings before retiring seven of the final eight batters he faced.
"I think it was more Yu Darvish not being in sync than anything," Scioscia said. "He was behind in a lot of counts, his pitch count was up. We got into some really good hitting counts against him, and we didn't miss some pitches."
C.J. Cron hit his third home run in as many days to give the Angels a 2-0 lead in the fourth inning. Four batters later, Kole Calhoun clanked a homer off the foul pole in right field to extend the Angels' lead to 5-0.
Darvish allowed at least four earned runs in consecutive starts for the first time since August 2012. He walked four and struck out nine.
"He's tough," Scioscia said. "He didn't quite have the same command today, but he's always managed a way to pitch us tough and beat us."
Shoemaker had a potential complete game in Cleveland cut short by a rain delay in the ninth inning. Over his last two starts, he is 2-0 with a 1.72 ERA and a 1.02 WHIP. The Angels won both games.
Shoemaker's 112 pitches were a career high.
"That was about the limits for Matt," Scioscia said. "I thought he pitched an outstanding game. That's a tough offensive lineup over there, and they're going to let you know when you miss spots. I thought he was on the money all [night], had control of counts."
"You've got to give him credit, he shut us down," Rangers manager Ron Washington said of Shoemaker. "He had a good breaking ball working. He threw strikes."
In each of his last six starts, Shoemaker has struck out at least six batters, the longest stretch of any Angels pitcher this season.
Calhoun scored in the bottom of the first to give the Angels a 1-0 lead when a crew chief review overturned the call on the field that ruled Calhoun out. As Calhoun was attempting to steal second, Albert Pujols lined a shot up the middle. Calhoun easily advanced to third and ran home when Leonys Martin's throw went up the third-base line.
Darvish collected the errant throw and threw home to beat Calhoun, but after review, the umpires ruled Rangers catcher Chris Gimenez blocked the plate before he had the ball, violating Rule 7.13. Washington was ejected for arguing the ruling.
The Rangers scored in the top of the sixth inning, when Shoemaker attempted to pick Elvis Andrus off first base. The throw bounced in the dirt and Cron could not locate the ball until Martin had raced in from third to end the shutout.
Brad Snyder homered off Joe Smith in the ninth for the Rangers' final run.