Vargas, who signed to a four-year $32 million contract in the offseason, allowed one hit and struck out one, throwing 13 strikes in 19 pitches.
"It went all right, I guess," Vargas said. "I was able to throw all my pitches and get acclimated to Salvy (catcher Salvador Perez) back there."
The Royals signed Vargas to replace Ervin Santana, who remains unsigned on the free agent market, in the rotation.
Gordon's double in the four-run third scored Christian Colon and Jarrod Dyson, who walked twice and scored a pair of runs.
Cameron Maybin, who was limited to 14 Padres games last year because of injuries, hit a long two-run homer in the third.
"It felt really good to crank one, just to kind of reassurance that the body feels well," Maybin said. "You always gain confidence when you put together some good at-bats. It was nice to get those high fives, slap everybody's hands. It was a long year for me last year not playing with injuries. It's just a nice feeling, feel like you're part of the game again."
Padres right-hander Ian Kennedy threw two scoreless innings, striking out two.
Kennedy limited the Royals to one hit -- Mike Moustakas' double -- in two scoreless innings. He threw 20 strikes in 26 pitches, striking out two and walking one.
"I threw a lot of fastballs, only a couple of changeups, one curveball and three sliders," Kennedy said. "I shook off a couple of off-speed pitches It is most importantly to get that fastball going, get the command going, especially the first couple of times out.
"It's the first time facing the hitter without a screen in front of you, so that was nice. I'm a little short (6-foot) for that screen with that bar right in front of my face. It's nice to throw to hitters and get that fastball established early."
PENNY'S MIXED BAG
Brad Penny, a National League All-Star in 2006-07 with the Los Angeles Dodgers, returned to the mound after sitting out last year. Penny, a 35-year-old right-hander who the Royals signed to a minor league contract, allowed three runs on five hits, including Maybin's long homer, in two innings. Despite the rough outing, Penny picked up the win.
Everth Cabrera, who was suspended the final 50 games last season for violation of the MLB drug prevention program, made his spring training debut, going 0-for-3. Cabrera was the Padres lone All-Star selection last year and was leading the National League with 37 stolen bases when he was suspended.
Royals second baseman Omar Infante has a stiff shoulder and was held out of the lineup for the second straight game and won't make the trip Sunday to play the Cubs.
"If it was the season, absolutely he'd be playing but with the rain and the weather the way it is, let the trainers get it all the way out of there," manager Ned Yost said.
The Royals signed left-handed pitcher Danny Duffy ($526,000), infielder Johnny Giavotella ($508,575) and outfielder Carlos Peguero ($504,250) to one-year contracts. None was eligible for arbitration. With those signings, all players on the Royals 40-man Major League roster are under contract.