Hardy went 4 for 5 to help Baltimore pull even atop the division with the New York Yankees, who lost 4-3 at Boston. The Rays are two games behind the co-leaders.
Chris Davis homered and Matt Wieters had three hits and two RBIs for Baltimore.
Hardy hit a two-run homer in the third inning, doubled and scored in the fifth, singled in a run in the sixth and added his 21st homer with a runner on in the eighth.
Baltimore starter Jason Hammel retired 11 of 13 Tampa Bay batters before leaving in the fourth inning with an injured right knee.
Steve Johnson (3-0) got the win with 1 1-3 innings of hitless relief.
Ryan Roberts and Elliott Johnson hit solo homers, and Matt Moore (10-10) allowed two earned runs on four hits and three walks in four innings for Tampa Bay.
RED SOX 4, YANKEES 3
BOSTON (AP) — Jacoby Ellsbury singled in the winning run in the ninth inning and Boston beat New York to drop the Yankees into a tie for first place in the AL East.
Pedro Ciriaco, who started the rally with a single, slid in to beat the throw from right fielder Ichiro Suzuki, giving Boston only its second win in 13 games.
The loss left the Yankees and Orioles tied with 79-62 records.
Andrew Bailey (1-0) got the win after allowing one hit in one inning.
David Robertson (1-7) retired his first four batters before giving up three straight singles with one out in the ninth.
TIGERS 5, WHITE SOX 3
CHICAGO (AP) — Doug Fister pitched seven innings of two-hit ball, Austin Jackson hit a tying two-run homer and Miguel Cabrera delivered a go-ahead solo shot as Detroit reduced Chicago's AL Central lead to two games.
Jackson's 14th homer followed a single by Omar Infante in the top of the fifth off Jake Peavy. One batter later, Cabrera hit his 36th of the season to put the Tigers up 3-2.
The only two hits Fister (9-8) gave up were solo homers to Dewayne Wise and Gordon Beckham.
Peavy (10-11) couldn't hold an early lead. He threw 117 pitches in 5 2-3 innings, yielding six hits, walking two and striking out nine.
RANGERS 6, INDIANS 4
ARLINGTON, Texas (AP) — Adrian Beltre homered, Matt Harrison worked into the sixth inning for his 16th victory and AL West-leading Texas beat Cleveland.
Harrison (16-9) struck out six over 5 2-3 innings while becoming the fourth AL pitcher to reach 16 wins. The left-hander allowed five hits and walked three.
Texas scored four times in the second, which started with Beltre reaching on an error that led to three unearned runs. One of those runs scored on the 16th wild pitch by Ubaldo Jimenez (9-16), who has the most losses and wild pitches in the majors.
Joe Nathan worked a perfect ninth for his 32nd save.
MARINERS 4, BLUE JAYS 3
TORONTO (AP) — Kyle Seager homered and came within a triple of the cycle, and Erasmo Ramirez pitched seven innings for his first major league win to lead Seattle over Toronto.
Starting for the first time since June 30, Ramirez (1-2) allowed two runs and six hits, setting down nine straight at one stretch. He walked one and struck out six. Four relievers combined to work the eighth and Tom Wilhelmsen closed it for his 25th save in 28 chances.
Seager had an RBI single in the first, doubled and scored in the third, and added his 18th homer in the fifth as the Mariners snapped a three-game losing streak.
Brandon Morrow (8-6) allowed four runs on 11 hits in 4 2-3 innings. He struck out four.
ROYALS 9, TWINS 1
MINNEAPOLIS (AP) — Will Smith pitched seven shutout innings and Eric Hosmer homered to lead Kansas City to a win over Minnesota.
Lorenzo Cain fell a home run shy of a cycle and had two RBIs to help the Royals beat the Twins for just the sixth time in the last 16 meetings.
Salvador Perez extended his hitting streak to a career-best 15 games and threw out two runners trying to steal in support of Smith (5-7), who struck out a career-high seven and gave up seven hits in his first win in four starts.
Scott Diamond (11-7) allowed four runs and 10 hits over six innings for Minnesota.
ATHLETICS 6, ANGELS 5
ANAHEIM, Calif. (AP) — Jerry Blevins got Howie Kendrick to ground into a game-ending double play with two runners on in the ninth inning and Oakland won its fifth straight.
Brandon Moss and Yoenis Cespedes homered and Dan Straily pitched into the seventh inning of his fourth major league start for the A's, who won their 11th straight road game, matching the second-longest streak in franchise history.
Torii Hunter and Albert Pujols had run-scoring singles in the ninth for the Angels, who had runners at the corners and no outs before Blevins relieved A's closer Grant Balfour and earned his first save since 2010.
Coco Crisp hit a ninth-inning RBI triple and scored on Hunter's error in right field for the A's, who have taken two straight at Angel Stadium with a rookie starter on the mound.
Blevins, who had just one save in his first 204 career appearances, struck out Kendrys Morales. Kendrick then grounded to third, and Oakland smartly turned the double play to end it.
Straily (2-0) yielded seven hits and struck out eight in his first start since coming up from Triple-A Sacramento last week.