Meadows, Randy Arozarena and Joey Wendle had three hits each, and Manual Margot and Yoshi Tsutsugo had three RBIs apiece as the Rays won their fifth straight. Tampa Bay entered the game hitting .220 as a team, just 23rd in the majors.
''We needed it,'' Rays manager Kevin Cash said.
The Rays roughed up starter Brad Keller (1-2) for five runs in 1 2/3 innings. Keller allowed three hits and walked three, including Lowe to load the bases on his final pitch.
''Tough, I can't pick up my defense when I walk three guys in an inning,'' Keller said. ''I was trying to do too much.''
Jake Newberry relieved and walked the next two batters to give Tampa Bay a 5-0 advantage.
''We came out and set the tone early on and got to Keller quickly,'' Cash said. ''We got some early runs with some good at-bats, not a lot of damage, but a lot of walks, taking advantage of count control.''
Carlos Santana homered and had two hits and three RBIs for the Royals.
''We've got a number of guys that are putting together good at-bats, but (Santana) is at the top,'' Royals manager Mike Matheny said. ''It'd be nice to get all the bats going at the same time.''
Tampa Bay rattled off another four-run inning in the sixth sparked by five straight hits from the heart of the batting order.
''As much a people want to talk about our pitching, but our hitting is pretty good, too,'' Lowe said.
Rich Hill allowed four runs in two innings for Tampa Bay. Andrew Kittredge (3-0) followed with a scoreless inning, and Trevor Richards pitched one-run ball over the last three innings for his first career save.
Zunino and Meadows hit back-to-back homers in the ninth.
Rays: RHP Cody Reed (left thumb weakness) was placed on the 10-day IL. Tampa Bay recalled RHP Brent Honeywell Jr. from the alternate training site. Honeywell tossed 1 1/3 innings, allowing one run, two hits and two walks.
Royals: Kansas City has had only three players spend time on the injured list this season. RHP Josh Staumont spent one day on the IL for a non-disclosed injury.
The Rays have yet to announce the starter for the series finale Wednesday. Jacob Junis (1-0, 1.50) will take the mound for Kansas City.
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