Scott Podsednik reached first base safely to start the ninth when Choate (0-2) misfielded a ball back to the mound. After Billy Butler singled and Jose Guillen was hit by a pitch, Alberto Callaspo gave the Royals a 2-1 lead with his sacrifice fly. Mitch Maier's single made it 3-1.
Evan Longoria nearly won it for the Rays in the bottom of the ninth, but his long drive to left with two runners on base was caught at the wall for a sacrifice fly, and Joakim Soria retired B.J. Upton on a fly ball for his sixth save.
Royals reliever Josh Rupe (1-1) threw a scoreless eighth to take the win.
In Detroit, Scott Sizemore and Brennan Boesch hit their first career homers in an eight-run fourth inning that powered Detroit over Los Angeles.
Sizemore's homer, which came one pitch after Gerald Laird's first of the season, tied the game 4-4. Miguel Cabrera added an RBI single later in the inning before Boesch's grand slam to center field.
Austin Jackson went 5 for 5, making him the first Tigers rookie with five hits in a game since Curtis Granderson in 2005.
Detroit starter Rick Porcello (2-2) won despite allowing five runs in 5 1-3 innings. Angels starter Joel Pineiro (2-3) gave up a career-worst 10 runs in 3 1-3 innings.
In New York, Derek Jeter hit a tiebreaking two-run triple in the seventh inning and drove in four runs to lift New York over Chicago.
With two on and one out in the seventh, Jeter sliced a pitch from Matt Thornton (2-2) past diving right fielder Jayson Nix and into the corner. Francisco Cervelli and Brett Gardner scored easily to give New York a 6-4 lead.
Jeter also hit a tying, two-run homer in the fifth for New York, which notched a third consecutive win. He went 3 for 4 and is batting .538 (7 for 13) in his past three games.
Paul Konerko set a White Sox record with his major league-best 11th homer in April and Gordon Beckham added two hits as Chicago lost for the 12th time in its past 14 games in New York.
Yankees reliever Alfredo Aceves (2-0) pitched a scoreless seventh to improve his career record to 13-1.
In Cleveland, Justin Morneau made an instant impact in his return to the Minnesota lineup, launching a two-run homer that helped Minnesota beat Cleveland.
After Joe Mauer singled with two outs in the first, Morneau - returning from two games out with a back injury - hit a 444-foot homer over the center-field wall against Fausto Carmona (3-1).
Kevin Slowey (3-2) moved up in Minnesota's rotation and pitched five innings for the win.
In Toronto, Alex Gonzalez hit two home runs and Vernon Wells also connected as Toronto crunched Oakland.
Gonzalez hit a three-run homer in the second inning and led off the sixth with a drive down the left-field line. It was the eighth multihomer game of his career.
Gonzalez has hit seven home runs this month, a team record for a shortstop in April.
Wells had three hits, including his eighth home run.
Toronto, which came in with an AL-leading 32 homers, sent the A's to their sixth straight road loss. Brandon Morrow (2-2) won.
In Seattle, Elvis Andrus scored from third on a wild pitch to break a scoreless tie in the top of the 12th inning as Texas beat a mistake-prone Seattle.
League (3-2) had retired all six Rangers he faced in the 10th and 11th innings, but he skipped a pitch off catcher Adam Moore's glove to allow Andrus to get home, and then Josh Hamilton had an RBI groundout for the only runs of the game.
Boom recruit Cliff Lee pitched seven scoreless innings in his Mariners debut.
Texas' Frank Francisco (3-3) pitched a wild 11th before Neftali Feliz finished for his fourth save in five chances.
Texas starter Colby Lewis went through nine scoreless innings, retiring 21 consecutive batters.
The Mariners had the bases loaded with one out in both the 10th and 11th innings. The latter came undone on a failed suicide squeeze by Seattle, which was followed by Texas manager Ron Washington's ejection.
In Baltimore, Adam Jones doubled and scored on a two-out single by Miguel Tejada in the 10th inning, giving Baltimore victory over Boston.
Tejada had three RBIs, including a tying homer in the eighth after Baltimore blew a 3-1 lead.
The win ended a seven-game skid for the Orioles against Boston at Camden Yards.
J.D. Drew hit two solo homers and Dustin Pedroia homered and drove in two runs for the Red Sox, whose three-game winning streak ended. The defeat left Boston with its first losing April since 1996.
Baltimore's Matt Albers (1-3) pitched a perfect 10th for the win.
Red Sox reliever Ramon Ramirez (0-1) took the loss.
