First baseman Mitch Moreland countered with a two-run homer for Texas in the first inning and finished with three RBIs on the day, but the Rangers pitching couldn't hold their early lead as their record fell to 1-6-1.
Peguero now has three homers, Saunders and Bay launched their second of the spring, and Morse got on the board with his first for a Mariners team looking to bolster its offense after finishing last in the American League in scoring the past four years.
"I don't think it's a conscious effort," Bay said of the long-ball parade. "It's just early on, we're getting good swings and balls are going out. I don't think that's how all the games are going to go. This is a little out of hand. But I think more than anything, it's just getting off to good starts, and we're hitting some balls well and we're going to go from there, myself included."
The seven straight Cactus League wins is the most by a Mariners team since 1998, as they improved to 7-1.
Right-hander Randy Wells, attempting to earn a spot in the Rangers' rotation as a non-roster invitee, gave up two runs -- one earned -- on five hits while needing 54 pitches to get through the first two innings.
Wells, 30, pitched the past five years for the Cubs, but missed the final eight weeks of 2012 with an elbow issue before signing a Minor League deal with Texas. He surrendered an unearned run in the first, when he walked Bay, gave up a single to Kendrys Morales and then saw Bay score when left fielder David Murphy bobbled Morse's base hit.
"Not the outing I want to have in a rotation battle, but you've got to build from it and tomorrow's a new day," said Wells, whose changeup -- ordinarily a go-to pitch -- let him down.
Peguero unleashed his third home run of the spring to lead off the second, taking Wells deep to right field. The 6-foot-5, 260-pound Peguero hit two home runs in his last start Wednesday against the Indians and is hitting .462 (6-for-13) with four RBIs in six Cactus League games.
Peguero also made a nice sliding catch on a bases-loaded line drive by Ian Kinsler in the fourth to help young right-hander Brandon Maurer escape a jam and then caught a deep drive at the left-field wall by Brandon Snyder in the seventh.
Mariners left-hander James Paxton, one of Seattle's top pitching prospects, gave up three runs on two hits and two walks in his first Cactus League start. Maurer replaced him and turned in two scoreless innings despite allowing two hits and two walks.
Rangers right-hander Cory Burns gave up the home runs to Saunders and Bay, with Morse then driving his blast off lefty Neil Cotts, who replaced Burns in the fourth. All three of those were two-run shots.
Texas trimmed the lead to 8-6 on a two-run double by Yangervis Solarte in the eighth.
The game was the first of three meetings this spring between the two American League West rivals, who square off again Sunday in Surprise.
Up next for Rangers: Righty reliever Jason Frasor will make his Spring Training debut against Arizona at 2:10 p.m. CT. The former Blue Jay signed with Texas during the offseason. But first, left-hander Matt Harrison gets the ball, making his second start of the spring as he looks to rebound from a rocky first outing.