Niemann (7-2) limited the Red Sox to four hits and an unearned run. He walked three and struck out five to win for the first time since a complete game shutout against Toronto on June 8.
Jason Bartlett drove in Tampa Bay's first run with a single off Felix Doubront (1-1) in the third. Sean Rodriguez tripled and scored on John Jaso's RBI grounder, giving the Rays a 2-1 lead in the fifth.
Carl Crawford's solo homer off Hideki Okajima added an insurance run in the eighth.
Daniel Nava drove in Boston's first run with a single off Niemann in the fourth. Four relievers held the Red Sox to one hit until Bill Hall walked and scored on Eric Patterson's two-out triple in the ninth off Rafel Soriano, who earned his 23rd save.
TAt Toronto, Denard Span drove in the go-ahead run with a single in the eighth inning for Minnesota.
Joe Mauer , Justin Morneau and Jason Kubel homered for the Twins. Delmon Young led off the eighth with a single off Jason Frasor (3-2). After a sacrifice, Scott Downs came on to face Span and allowed his RBI single to center.
Young went 3 for 3 with an RBI and an intentional walk and is batting .363 since June 3.
Jose Mijares (1-0) retired two batters for the win. Jon Rauch worked the ninth for his 19th save.
At Detroit, Johnny Damon followed his 2,500th hit with a game-winning homer in the 11th inning for Detroit.
Austin Jackson led off the inning with a single off David Hernandez (3-7) and Damon followed with a long homer to right. Damon singled in the third inning for his 2,500th hit, and received an ovation from the crowd of 22,532.
Ryan Perry (2-4) got the win with a scoreless inning of relief.
The Tigers trailed 4-1 going into the eighth, but Miguel Cabrera led off with a triple and scored on Brennan Boesch's single. Brandon Inge's one-out triple scored Boesch to make it 4-3. After an out, Ramon Santiago walked, but pinch-hitter Austin Jackson bounced out to end the inning. Julio Lugo made it 5-3 Baltimore with an RBI single in the ninth.
At Arlington, Texas, Josh Hamilton homered to stretch his home hitting streak to 26 games, and C.J. Wilson pitched six strong innings for Texas.
Vladimir Guerrero added a two-run homer in a five-run sixth inning, Nelson Cruz and David Murphy also went deep, and Joaquin Arias had a career-high four RBIs for Texas.
The game was delayed for 16 minutes in the fifth inning when a male spectator fell about 30 feet from the second deck while attempting to catch a foul ball. The team said he was "able to move all his extremities and was responsive to paramedics."
The AL West-leading Rangers won after losing five of seven.
At Chicago, Andruw Jones hit his 399th career home run and Chicago won despite losing starter Jake Peavy in the second inning because of a back injury.
Alex Rios added a solo homer and drove in two runs for the White Sox, who are a major league-best 20-5 since June 9 and are a season-high six games over .500 (44-38).
White Sox reliever Tony Pena (2-1) picked up the win, allowing one run and five hits in 4 1-3 innings. Bobby Jenks got his 18th save in 19 opportunities.
Torii Hunter had three singles for the Angels, who have lost four of five.
At Oakland, California, New York's Alex Rodriguez hit his 21st grand slam and added a solo shot for his 597th home run, helping CC Sabathia win his seventh straight.
Rodriguez connected with the bases loaded in the third inning to tie Manny Ramirez for the second most slams, then went deep again in the sixth off Trevor Cahill (8-3) to lead the Yankees to their fourth straight win.
A-Rod has 21 home runs at the Coliseum, the most by a visiting player.
Sabathia (11-3) got the best of a matchup between All-Star pitchers. Sabathia allowed one run and seven hits in 7 2-3 innings.
Trevor Cahill (8-3), who had won seven straight decisions, allowed six runs, the most he has given up since his first start of the season, April 30 at Toronto.
New York's nine grand slams are one shy of the club record set in 1987.
At Seattle, Kansas City's Zack Greinke allowed two hits over seven innings and continued his mastery of Seattle.
Greinke (5-8) is 4-0 with a 1.64 ERA in 10 career appearances against the Mariners. Last Aug. 30, he tossed a career-best one-hitter at Safeco Field, retiring the final 22 Mariners in a row.
Wilson Betemit drove in all the runs for the Royals on a fifth-inning home run, a two-out, bases-loaded infield single in the sixth and a two-out RBI single in the eighth.
Joakim Soria worked the ninth to pick up his major league-leading 24th save.
Greinke, who has won four straight decisions, held the Mariners without a run for the first three innings to set the franchise record for consecutive scoreless innings against one team. He kept the Mariners off the scoreboard for 31 consecutive innings, two more than Paul Splittorff against the Chicago White Sox from September 1972 to July 1973.
A fan interference call in the eighth inning may have prevented the Mariners from tying the game. Jack Wilson scored on a sacrifice fly by Chone Figgins that made it 3-2 with two outs and Ichiro Suzuki on first.
Russell Branyan then hit a double down the right-field line but a young fan leaned over and touched it. Suzuki's speed likely would have allowed him to score from first but the umpires ruled a ground-rule double and Suzuki returned to third. Jose Lopez ended it with a groundout.
The Mariners broke Greinke's scoreless spell when Michael Saunders opened the third with an infield single and moved to second when second baseman Aviles through wildly to first. Josh Bard's right-side groundout advanced Saunders to third.
Jack Wilson then squared on Greinke's first pitch and pushed a bunt toward first. It was a safety-squeeze, as Saunders held up momentarily. Greinke covered the bunt but didn't even look at the plate. He threw to first as Saunders scored.
