The free-agent acquisition worked seven innings, allowing one run on only three hits, in his debut in a Mariners uniform.
Silva got an assist from fifth starter Miguel Batista, who was pressed into closer duties after All-Star reliever J.J. Putz was placed on the 15-day disabled list earlier in the afternoon. He has inflammation in the cartilage that is attached to the rib cage.
"An interesting way of using your bullets," the former Blue Jays' closer said of picking up his first save since 2005. "Going out there tonight and trying to ensure Carlos' first win was a little -- I wouldn't say nerve-breaking -- but there was a concern. The guy did such a job, you want to make sure you don't give too much of a good pitch."
Batista retired all three batters he faced after Sean Green walked Josh Hamilton to lead off the ninth inning.
Ian Kinsler led the game off with a double off Silva, but the right-hander settled in nicely after that, not allowing another hit until former Mariners first baseman Ben Broussard hit a home run in the top of the sixth, cutting Seattle's lead to 4-1.
"I was so nervous," Silva said of his Seattle debut. "I wanted to do so good, but I tried to relax, be myself and pitch my game."
The only other hit the right-hander allowed on the night was a one-out double in the seventh inning to Milton Bradley. Silva was able to escape that threat when he induced a popup in the infield off the bat of Gerald Laird. That came on Silva's 116th and final pitch of the evening.
"Silva was spectacular," manager John McLaren said. "You can't pitch much better that that. He was fabulous."
"You have to give credit to Silva," Texas manager Ron Washington said. "The guy kept us off-balance, that's what he does. He changed speeds, kept the ball down, got a lot of ground balls. We had him in a lot of 3-2 counts, but then he made pitches when he had to."
Designated hitter Jose Vidro gave Silva an early cushion with his first home run of the season, a solo shot off Texas starter Jason Jennings in the bottom of the third inning. Jose Lopez added a three-run home run in the bottom of the fifth inning to give the Mariners a 4-0 lead.
"Silva threw unbelievably out there. He was in command pretty much the whole game," Vidro said. "The spots where he was in trouble, he made the good pitches to get out of the inning. And the Lopez home run gave [him] more room to work with. It was good.
"After a tough loss last night, we came back strong today, won the ballgame and won the series to start the season. It's a good way to go."
Silva followed the lead of Seattle's first two starters, Erik Bedard and Felix Hernandez. The trio has allowed only two earned runs in 19 innings of work, helping the Mariners win the season-opening series, 2-1, over their division rival.
"This is what everybody was expecting from the starters," Silva said.
Chris Hester is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.