"This is Matsui's day," Jeter said, "so everyone needs to focus on him."
Jeter's homer was the Yankees' first long ball by a right-hander since June 25, and his presence appeared to give the team an immediate lift.
"Just wave the magic wand," Andy Pettitte said. "It was cool."
After he homered and gave a quick wave of his cap from the dugout steps, Cano singled and Soriano followed with his first hit with New York in nine at-bats. Vernon Wells had a sacrifice fly and Suzuki had RBI single to make it 3-0.
Jeter started at shortstop for the first time this year. He was the designated hitter on July 11 when he returned from rehabbing the ankle he first broke during the opener of the AL championship series in October. He was sent right back to the disabled list when he strained his right quad running out a grounder. The Yankees won just four of 12 during his most recent absence.
"He's the face of the organization," Soriano said. "When he's on the field we can feel the energy."
Jeter's take: "It was fun — I'm tired. I worked hard to try to get back on the field."
Johnson, who drove in the run in Tampa Bay's 1-0 win Saturday, pulled Tampa within two on a double in the second and Tampa took the lead in the third.
Evan Longoria and James Loney singled with one out, then Myers laced a shot to deep left for a 4-3 edge.
But in the bottom half, Jeter opened the inning by lining a single that glanced off Johnson's glove behind second base. Girardi was concerned Jeter would overdo it on the bases, but the 13-time All-Star only needed another easy jog to score his second run.
Soriano sent him into a trot, eking a homer over the right-field wall just out of the reach of a leaping Myers.
"If I had one more step, I feel like I could catch that ball," Myers said.
Myers put another ball of his own out of everyone's reach in the fifth, an opposite-field shot to right for the first multihomer game of his career.
Plagued by home runs throughout his career, Hughes has allowed 20 this season. Often mentioned in trade rumors, Hughes yielded five runs and nine hits in four-plus innings and left to a vociferous Bronx cheer.
He was lifted after walking Matt Joyce in the fifth, and the New York bullpen shut down the Rays the rest of the way. Preston Claiborne, Boone Logan, David Robertson and Rivera combined on five innings of one-hit ball.
Moore's six-start winning streak ended when he was lifted after five innings with the score tied at 5. Moore allowed five runs and eight hits.
NOTES: Myers has a nine-game hitting streak. ... Yankees RHP David Phelps (forearm strain) said he will make his second rehab start Tuesday, for Double-A Trenton. ... Injured INF 3B Jayson Nix (strained right hamstring) should be activated when the Yankees visit the Dodgers on Tuesday. ... Rays INF Ben Zobrist was given the day off. ... Yankees OF Curtis Granderson (broken left pinkie), who could rejoin the team next weekend, was hitless in four at-bats, including two strikeouts, in his fourth game with Class A Tampa. He is 2 for 13 overall. ... A-Rod arrived at the Yankees complex in Tampa, Fla., around 5 p.m. and took BP and fielded grounders on the grass after the Tampa Yankees game.