Vargas (1-3) threw 107 pitches in his sixth start for the Angels, striking out three and walking two while getting 15 groundball outs. The shutout was the fourth by the left-hander in 136 career starts and his ninth complete game.
"I guess I take more satisfaction just in the way we played the game and the way we were able to be so efficient out there without really giving them an opportunity to put together a big inning," Vargas said. "The plays that we made out there early and late really just set us up for success."
Vargas did not allow a hit until J.J. Hardy slapped an opposite-field single to right with two out in the fifth. The left-hander walked his next batter, Steve Pearce, on four pitches before Alexi Casilla grounded out.
"It was one of those games where the balls they hit hard happened to go at people," said Vargas, who retired his first four batters on fly balls. "But if you can control the count and control the hitter, you're going to have the upper hand."
The Orioles got a runner to third base in the seventh when Adam Jones led off with a double and advanced on a groundout by Ryan Flaherty, who had replaced first baseman Chris Davis in the fifth after the Orioles' home run and RBI leader injured his right knee. But Jones was tagged out in a rundown by third baseman Alberto Callaspo, who fielded Hardy's grounder as Jones went on contact.
Vargas lowered his ERA to 1.63 against the Orioles in seven starts against them, his best against any team.
"He's one of those guys that you know what he's going to do coming in," Orioles manager Buck Showalter said. "I thought when they made that acquisition in the off-season, it was one of the better ones made under the radar. They'll like him before the season's over."
Baltimore's only other hit was a one-out double in the ninth by Nick Markakis. But Vargas ended it by striking out Adam Jones and retiring pinch-hitter Chris Snyder -- fittingly enough -- on a grounder to third base.
"He's a competitor, man," said Angels injured ace Jered Weaver, who has known Vargas since they were teammates at Long Beach State. "He had some good stuff at Long Beach. He was like a 94 guy in college, but we all know that that doesn't last forever. He's turned himself into a pitcher now. He's not a thrower like he was in college."
Miguel Gonzalez (2-2) gave up three runs and six hits over six innings and struck out five without walking a batter. The right-hander's outing was shortened by a blister on his thumb.
"He could have maybe finished the game," Showalter said. "We've got an off day next week, so we can give him an extra day. But we'll see if he'll miss that start. It's a pretty deep blister. He ripped the top off of it."
Gonzalez retired the side on just five pitches in the first inning, but Trumbo drove his first offering of the second to left-center for his seventh home run and fourth in five games.
"I guess at times I can be kind of streaky," said Trumbo, who had a four-game home run streak last season. "If you're aggressive within an area, then you can check off some of the pitches that you can't handle."
The Angels got a runner to third base in the third, when Erick Aybar doubled with two out and advanced on a wild pitch. Gonzalez escaped the jam by striking out Trout, but last season's AL Rookie of the Year made up for it his next time up in the fifth with a drive over the left field fence.
Trout made it 4-0 in the seventh with an RBI single.
Gonzalez was signed as an undrafted free agent by the Angels in December 2004, but never played for the big club. His first big league start came against them on July 6, 2012 at the Big A, allowing a run over seven innings in a 3-2 victory. During that game he wore a glove given to him by minor league teammate Nick Adenhart, who was killed by a convicted drunk driver in 2009.
Mark Leiter Jr., the son of the former Angels pitcher, struck out 20 batters Friday night for New Jersey Institute of Technology in a 5-3 victory over Chicago State. He was only 3 years old when his infant brother Ryan died of spinal muscular atrophy in April 1994, just as their father was beginning his only season with the Halos. ... Callaspo returned from the disabled list after missing 19 games with a bruised left heel. The Angels optioned INF Andrew Romine to Triple-A Salt Lake. ... RHP Jerome Williams will make his first start of the season on Sunday instead of RHP Garrett Richards, who is back in the Angels' bullpen after going 1-2 with a 5.54 ERA in four starts in Weaver's place. Williams' first eight appearances were in relief, including a six-inning stint at Oakland on Monday night, when he pitched the 10th through 15th innings and gave up an unearned run in a 19-inning loss.