New York's Yankees, Philadelphia and Cincinnati all gained a full game Tuesday night.
The Yankees beat Tampa Bay to gain a 2 1/2-game lead in the America League East.
Philadelphia stretched its lead to five games in the National League East by beating Atlanta.
Cincinnati's victory, coupled with St. Louis' loss, enabled the Reds to go eight games up in the NL Central.
Yankees 8, Rays 3 _ Nick Swisher homered off James Shields to key a five-run burst in the first inning for New York.
The Yankees cut their magic number for clinching a playoff spot to three over Boston.
Tampa Bay nicked Phil Hughes (17-8) and relievers Javier Vazquez and Joba Chamberlain but never quite got the big hit it needed while stranding 10 runners.
Ahead 7-3, Chamberlain escaped a bases-loaded jam in the eighth by striking out pinch-hitter Brad Hawpe and getting John Jaso on a liner to center. Chamberlain finished for his third save.
New York has won the first two in this four-game series, and pulled even at 8-all with the Rays this season.
Robinson Cano blooped an opposite-field, two-run double to left in front of a diving Carl Crawford for a 7-3 lead in the seventh. Derek Jeter doubled home a run in the eighth.
Shields (13-13) started against the Yankees for the sixth time this season. He had done well in his previous outings, but this time they figured him out in a hurry. It's a pattern that's troubled the Tampa Bay rotation for the last few weeks — aside from ace David Price, Rays starters have struggled
A bright moon hung over the right-field facade when the game began, and Swisher hit a rocket into the bleachers on Shields' sixth pitch for his 27th homer. Jorge Posada hit an RBI single with two outs, Lance Berkman boomed a two-run double and Curtis Granderson's single made it 5-0.
Phillies 5, Braves 3 _ Roy Halladay became Philadelphia's first 20-game winner in 28 years, and Jayson Werth hit a three-run homer for Philadelphia.
Halladay (20-10) allowed three runs and seven hits in seven innings to reach 20 wins for the third time in his career. Hall of Famer Steve Carlton was the last to do it for the Phillies when he won 23 in 1982. Robin Roberts, another Hall of Famer, was the last right-hander to win 20 for Philadelphia, in 1955.
The two-time defending NL champions are 43-15 since July 21, when they trailed the Braves by seven games. They are 17-3 in September.
The Phillies reduced their magic number to clinch the division to six.
Rookie Mike Minor (3-2) lasted just 2 1-3 innings in his eighth career start, allowing three runs and seven hits.
Atlanta's Freddie Freeman hit his first major league homer, a solo shot off Halladay in the seventh. Freeman was 1 for 13 before he connected.
Ryan Madson tossed a scoreless eighth for Philadelphia and Brad Lidge finished for his 25th save in 30 chances.
Reds 4, Brewers 3 _ Edinson Volquez continued to make his case that he should be a big part of Cincinnati's postseason rotation by allowing one run over eight innings.
Jim Edmonds homered before hurting himself rounding the bases and the Reds didn't make it easy in the ninth.
Closer Francisco Cordero converted his 38th save, but two runs scored with two outs on a pair of errors when right fielder Jay Bruce made a wild throw that also went through Cordero's legs.
The Reds need any combination of four wins or four losses by the Cardinals to clinch the NL Central.
Pirates 5, Cardinals 2 _ Paul Maholm became the latest slumping pitcher to shut down the fast-fading Cardinals, pitching effectively over seven innings, and Pittsburgh won its season-high fourth in a row.
The Pirates remain two losses way from their first 100-loss season since 2001, but are 4-0 on a homestand that began with a three-game sweep of Arizona. Pittsburgh hadn't won four straight since a five-game run from Aug. 17-22, 2009, against the Brewers and Reds.
For the Cardinals, it was their 24th loss in 36 games.
The Cardinals probably didn't see this coming when they were in first place on Aug. 14, a few days after sweeping three in Cincinnati, but their season has come undone against teams and pitchers with poor records. They have dropped their last seven series against teams under .500, losing two of three during their last visit to Pittsburgh from Aug. 23-25.
They also keep being beaten by pitchers with elevated ERAs. A day after losing 4-0 to Florida's Chris Volstad, who began the game with a 5.11 ERA, they couldn't get to Maholm (8-15), who came into his 31st start of the season with a 5.36 ERA and a six-game losing streak.
Others who have beaten St. Louis recently include John Lannan, Jeff Samardzjia and Chris Narveson.