Kansas City has scored just one run in losing the first two games of the four-game series. The Royals were hitless in five at-bats with runners in scoring position Tuesday and are 2 for 17 over the last two games.
"We had a couple chances," Kansas City right fielder Jeff Francoeur said. "Guys like Shields, you get a guy on third and that's when those guys become their best."
The lack of offense wasted a solid effort by Jeff Francis (4-12), who gave up four runs and five hits over seven innings. The left-hander retired 15 in a row after allowing the first three batters to reach base in the first.
"It feels frustrating because he pitches a great game," Francoeur said.
Francis struck out four.
"I felt about as good as I've felt this year," Francis said. "James Shields kind of just stole the show. He was pretty stellar."
Shields (11-9) also has four shutouts this year. The right-hander is 6-2 in nine career starts against Kansas City.
"James Shields, wow, really good stuff," Tampa Bay manager Joe Maddon said.
Longoria drove in two runs on a single during the first and hit a two-run homer in the sixth. He has driven in 12 runs over his last 12 games despite having just nine hits during the stretch.
The game had a three-man umpiring crew because crew chief Derryl Cousins was unavailble due to a personal medical issue. His replacment, Chris Conroy, didn't make it to the ballpark in time to take the field.
The time of the contest was 1 hour, 53 minutes — the fastest nine-inning game in Tampa Bay history.
Longoria put the Rays ahead 2-0 with his two-run single in the first. Desmond Jennings was hit by a pitch and Johnny Damon had a bunt single, and both later scored on Longoria's hit after a double steal.
"You take Longoria out of their lineup and we're still playing," Royals manager Ned Yost said. "But obviously you can't do that."
Melky Cabrera was caught stealing at second in the fourth after Billy Butler struck out looking on a 3-2 pitch. The next batter, Eric Hosmer, walked and became the first player to steal a base this season with Shields pitching when he stole second.
Damon, who entered mired in a 2-for-31 slide, had two hits in four at-bats. The designated hitter, with 2,682 career hits, moved within one of tying George Davis for 65th place on the all-time list.
Notes: The Royals have been shutout six times this season. ... Kansas City LF Alex Gordon is 1 for 45 in 13 games at Tampa Bay. ... Shields was the fifth consecutive starting pitcher with double-digit wins this season that the Royals have faced. ... Kansas City RHP Felipe Paulino (1-4), Wednesday's scheduled starter, has 49 strikeouts and 11 walks — two intentional — in his last seven outings. ... Tampa Bay RHP Wade Davis (8-7) will look to improve on his early-inning struggles in his start on Wednesday. "That's going to be my main goal, to go out and get through it a lot better this time," Davis said. He has overcome bad first innings in his previous two starts to pitch six and 7 2-3 innings, respectively.