Fielder ended a 13-game homerless streak to start the season with a line drive to right-center field off former Texas first-round pick Blake Beavan (0-1) to lead off the second inning. Two pitches later, Kouzmanoff went deep to left.
Told before the game that he was a game away from tying the longest drought to start a season in his career, Fielder casually figured it was about time for a long ball.
"I was just messing around," said Fielder, in his first season with the Rangers after a trade that sent fan favorite Ian Kinsler to Detroit. "But I guess it worked."
The Mariners didn't get a runner past second base in their third shutout loss in a week.
"Probably the first night where I was probably a little disappointed in our approach a little bit," Mariners manager Lloyd McClendon said. "I thought we should have done better."
Kouzmanoff also had two doubles, the second one driving in two runs to put the Rangers up 4-0 in the eighth inning. Fielder scored from first base after he was intentionally walked following a pair of strikeouts.
Ross (1-0), a former reliever, got his first win as a starter in his third try as the Rangers recorded their third straight win by shutout and fourth in seven victories overall.
Fielder's homer was the first run the Rangers scored with Ross on the mound. He had gone 12 1/3 innings without Texas scoring, tops in the majors.
"It's funny because I'm just trying to go out there and do the best I can to keep it close because I know we're going to start scoring," said Ross, who has allowed two earned runs in 18 innings as a starter.
Ross struck out Abraham Almonte and Brad Miller to start the game, but didn't have another strikeout. After Robinson Cano and Corey Hart followed with singles, Ross ended the first inning on Stefen Romero's groundout to short -- the first of seven straight outs on grounders and 16 overall.
The left-hander didn't walk anybody in 7 2/3 innings, but hit Miller with a pitch twice. The second one made Cano the potential tying run in the eighth, but Ross got him on a flyout to center before Alexi Ogando replaced him.
"I think he was able to get in on us and I guess kind of mix it up," Miller said. "We really just didn't string together our good at-bats often, but credit to him."
Beavan was called up from Triple-A Tacoma to fill in for rookie left-hander James Paxton, who is out with a strained muscle in his back. He gave up six hits -- the other four besides the homers were singles -- in four innings with one strikeout. He came out for Dominic Leone because of shoulder soreness.
The right-hander who grew up in nearby Irving spent most of last season with Tacoma after losing his spot in the rotation after two starts. It was his first start since April 10, 2013, and first appearance since a relief outing last July 9.
It will be a battle of aces Wednesday night when Seattle's Felix Hernandez facing Texas' Yu Darvish. The Japanese right-hander is the first AL starter since Hernandez in 2007 to begin the season with two starts of at least seven shutout innings in April. Darvish lost to Hernandez twice during his rookie season in 2012. They didn't face each other last year. ... The Rangers had multiple homers in a game for the first time this season. They went deep just twice in their first seven home games. ... The Mariners had a double play that went down as a routine 6-4-3, but was far from it. The ball caromed off shortstop Miller's glove straight to Cano just as he was getting to second base, and Cano made the easy throw to first.