Moore (7-0) yielded a three-run homer to David Ortiz in the first, then limited the struggling Red Sox to one hit over the next five innings.
The Rays overcame the early deficit with a five-run fifth off John Lackey (1-4). Jose Molina and Matt Joyce each drove in two runs in the inning, helping Tampa Bay extend its winning streak to a season-high six games.
Boston has lost six of seven, including three straight.
Moore allowed three hits and struck out eight. The 23-year-old lefty matched Washington's Jordan Zimmerman for the major league lead in victories, became the first Tampa Bay starter to begin a season 7-0 and tied a club record by winning his eighth straight decision dating to September.
Fernando Rodney struck out the side in the ninth to finish the combined three-hitter and earn his seventh save.
YANKEES 4, MARINERS 3
NEW YORK (AP) — Robinson Cano hit a two-run double, Lyle Overbay delivered a tiebreaking sacrifice fly and New York rallied past Seattle after Felix Hernandez left following a couple of odd twists.
Hernandez exited after six innings with a 3-1 lead, having outpitching CC Sabathia in the first matchup between the former Cy Young Award winners. Hernandez, however, tweaked his back in the sixth when he fielded a comebacker, pivoted and threw to second for a forceout.
The right-hander allowed one earned run in another strong outing at Yankee Stadium, and leads the AL with a 1.53 ERA. Sabathia, who had won his last eight starts against Seattle, struck out 10 in 6 1-3 innings while giving up 10 hits.
Raul Ibanez hit a two-run homer for Seattle in his return to Yankee Stadium. New York star Curtis Granderson came off the disabled list and went 0 for 3 with a walk in his season debut.
Down 3-1, the Yankees rallied for three runs in the seventh to win for the seventh time in eight games.
Charlie Furbush (0-2) gave up Cano's tying double off the base of the wall in right-centre.
Shawn Kelley (2-0) got two outs and Mariano Rivera remained perfect in 16 save chances this season.
RANGERS 6, ATHLETICS 5, 10 INNINGS
OAKLAND, Calif. (AP) — Adrian Beltre hit a tiebreaking home run in the 10th inning, Mitch Moreland followed with his second of the game and Joe Nathan made sure Texas held off Oakland.
Nathan gave up a run in the bottom of the 10th but escaped a bases-loaded, one-out jam to snap Texas' four-game losing streak to the Athletics.
Beltre sent a 3-0 pitch from Chris Resop (1-1) to centre field with one out in the 10th for his ninth homer of the year. Moreland connected two batters later. He also hit a two-run shot in the fourth.
Nathan needed 31 pitches to nail down his 12th save in as many chances this season. After a pair of one-out walks, Seth Smith doubled in a run. Nathan intentionally walked Brandon Moss before striking out Daric Barton. The closer then retired pinch-hitter Eric Sogard on a first-pitch groundout to end it.
Tanner Scheppers (3-0) pitched two scoreless innings for the win. Nelson Cruz's second sacrifice fly of the game tied it in the eighth against Ryan Cook.
A's manager Bob Melvin was ejected for the third time this season.
ANGELS 6, ROYALS 2
ANAHEIM, Calif. (AP) — Albert Pujols, Howie Kendrick, Josh Hamilton and Mike Trout all homered off Jeremy Guthrie, and Los Angeles handed the Kansas City right-hander his first loss in 19 starts.
Hamilton, the Angels' right fielder, made his fourth start at designated hitter after being removed from Monday night's series-opening loss in the seventh inning because of lightheadedness.
Guthrie (5-1) yielded five runs and 11 hits over seven innings. He held the franchise record for consecutive starts without a loss while winning his previous 10 decisions. It was his first loss since Aug. 3 last year, when Texas beat him 5-3 at Kansas City.
It was the first time in Guthrie's 10-year career that he allowed four homers in a game.
Jason Vargas (2-3) gave up five hits in seven-plus innings and struck out seven. Both runs against the left-hander were knocked in by Billy Butler, who homered and had an RBI double.
TIGERS 6, ASTROS 2
DETROIT (AP) — Miguel Cabrera homered, Doug Fister pitched seven impressive innings and Andy Dirks gave the Tigers a lift for a second straight night in Detroit's victory over Houston.
Dirks hit a grand slam in Monday's win over Houston, and a night later he capped a three-run fifth with a tiebreaking double. The Tigers added two more runs in the sixth, and Cabrera hit his eighth homer in the seventh, a solo shot that gave Detroit a 6-2 lead.
Fister (5-1) allowed two runs and five hits. He struck out seven without a walk.
Lucas Harrell (3-4) gave up five runs and seven hits in five-plus innings. The Astros have lost six straight and 16 of 19.
WHITE SOX 4, TWINS 2
MINNEAPOLIS (AP) — Adam Dunn and Dayan Viciedo hit consecutive homers to back another strong start from Jake Peavy in Chicago's victory over Minnesota.
Peavy (5-1) gave up two runs and five hits in seven innings and Tyler Flowers' double in the eighth scored the go-ahead run for the White Sox. Addison Reed earned his 12th save.
Kevin Correia (4-3) allowed four runs and nine hits in seven innings.
BLUE JAYS 10, GIANTS 6
TORONTO (AP) — R.A. Dickey snapped a four-start winless streak, Melky Cabrera had four hits against his former team and Toronto beat San Francisco.
Edwin Encarnacion drove in two runs and scored twice as the Blue Jays had a season-high 18 hits and won three straight games for the second time this season.
Dickey (3-5) struck out a season-high 10 in six innings, allowing two runs and six hits, to win for the first time since April 18 against the White Sox.
Brandon Belt hit a solo homer and Pablo Sandoval added a three-run shot in the ninth but it wasn't enough for the NL West-leading Giants, who had won three straight and 10 of 13.
Cabrera went 4 for 5 with two RBIs. He reached on an error and hit an RBI single in Toronto's six-run first inning.
Before the game, Giants manager Bruce Bochy presented Cabrera with his 2012 World Series ring in a private ceremony in the weight room. The MVP of last year's All-Star game, Cabrera was suspended 50 games Aug. 15 for a positive testosterone test, and was later left off San Francisco's post-season roster. He signed a two-year, $16 million deal with Toronto in November.
Barry Zito (3-2) allowed eight runs, five earned, and a season-high 12 hits in 5 2-3 innings.
PADRES 3, ORIOLES 2
BALTIMORE (AP) — Chris Denorfia and Everth Cabrera hit two-out RBI singles off Jim Johnson in the ninth inning, and San Diego got a home run from Carlos Quentin in a victory over Baltimore.
After the Orioles took a 2-1 lead in the eighth, Johnson (1-3) entered with a franchise-record streak of 35 straight converted saves. He immediately gave up two consecutive singles before getting Jedd Gyorko to hit into a 6-4-3 double play. But Denorfia followed with a single up the middle and, after Johnson hit Nick Hundley with a pitch, Cabrera singled to centre for a 3-2 lead.
Luke Gregerson (2-2) got the last out in the eighth and Huston Street earned his ninth save. The Padres were 0-18 when trailing after eight innings.
Ryan Flaherty homered for the Orioles, who fell to 18-2 when leading after eight.