A's won American League West, beating Texas Rangers, and the Yankees thrashed Boston Red Sox to take the AL East.
MLB: Oakland Athletics and the New York Yankees win divisions
The Oakland Athletics and the New York Yankees signed off in style with big wins as they clinched American League divisional titles on the final day of the regular season.
The A's landed the AL West title by toppling long-time leaders the Texas Rangers 12-5 at the Coliseum, and the Yankees crushed the Boston Red Sox 14-2 in New York to tie up the AL East.
Having trailed Texas by 13 games at one stage this season, Oakland had been steadily clawing back that lead and entered the last night on level terms with the Rangers.
It meant their tussle was winner-takes-all, and briefly it seemed Texas were destined to capture the title after all, as they surged 5-1 in front.
The lead was swiftly wiped out though as Oakland completed a sweep of the series to reach the post-season as divisional champions and leave their visitors resigned to a wild-card play-off clash against the Baltimore Orioles on Friday. Texas will have home advantage in Arlington.
Oakland's stunning improvement in the second half of the season now sees them head into the business end of the year on a six-match winning run.
When AJ Griffin gave up five runs at the top of the third inning, it looked as though Oakland's spectacular recovery may have run its course.
Yet Oakland took six runs from Ryan Dempster and Derek Holland in the fourth inning, going ahead when Josh Hamilton at centre field dropped a catching chance and allowed two through to score.
Derek Norris lifted Oakland four clear with a home run in the eighth, and Texas offered little in response.
The Yankees knew they had the AL East in the bag before their one-sided contest with Boston finished, after nearest rivals Baltimore stumbled to defeat against the Tampa Bay Rays.
Curtis Granderson and Robinson Cano both homered twice for New York.
Evan Longoria went one better for Tampa Bay in their 4-1 win over Baltimore.
His three homers denied a side who had to win and hope for a stunning upset in New York, where Boston, bottom of the AL East, were unable to turn around a seven-match losing streak which stretched to eight as their campaign reached a dismal conclusion.
For the first time since 1967, when Boston's Carl Yastrzemski achieved the feat, the major leagues have a Triple Crown winner.
Miguel Cabrera of the Detroit Tigers finished the regular season as the player with the highest batting average (.330) and most home runs (45), and as RBI leader (139). The 29-year-old Venezuelan is a seven-time All-Star and was cheered by the Kansas City crowd during Detroit's 1-0 victory over the Royals. Detroit had already secured the AL Central title.
MLB commissioner Bud Selig led the praise, saying: "It is an honour to congratulate Miguel Cabrera on earning the Triple Crown, a remarkable achievement that places him amongst an elite few in all of baseball history.
"Miguel has long been one of the most accomplished hitters in the game, and this recognition is one that he will be able to cherish for the rest of his career in baseball and beyond.
"As the Tigers prepare for the post-season, we have a global stage to witness Miguel's talent, which will go down as one of the hallmarks of Major League Baseball's extraordinary 2012 regular season."
The Toronto Blue Jays edged out the Minnesota Twins 2-1 to sweep their three-game series, as Venezuelan former All-Star shortstop Omar Vizquel brought his career to an end at the age of 45 and finished on a winning note.
Casper Wells had a three-run homer in the Seattle Mariners' 12-0 win over the Los Angeles Angels and Dan Johnson hit three home runs in the Chicago White Sox's 9-0 trouncing of the Cleveland Indians.
There were fewer issues to decide in the National League.
NL East winners the Washington Nationals rounded off their regular-season campaign with a 5-1 win over the Philadelphia Phillies.
Washington will have home advantage through the post-season owing to their major league-high total of 98 victories.
The Atlanta Braves warmed up for Friday's wild-card clash with the St Louis Cardinals by defeating the Pittsburgh Pirates 4-0.
St Louis also won, in their case 1-0 against NL Central champions Cincinnati. The Reds were on 97 wins heading into the contest but could not match Washington's season total.
The Los Angeles Dodgers finished their season on a high with a 5-1 win against NL West winners the San Francisco Giants, while the San Diego Padres beat the Milwaukee Brewers 7-6 and the Colorado Rockies overcame the Arizona Diamondbacks 2-1.
In matches between teams who had long given up hope of reaching the post-season, the Chicago Cubs squeezed home 5-4 against the Houston Astros while the New York Mets beat the Miami Marlins 4-2.