The Tigers tied up the American League Central title and the Nationals, even in defeat, were able to clinch the National League East top spot.
Miguel Cabrera's 44th homer of the season in a five-run sixth inning helped Detroit beat the Kansas City Royals 6-3, with Jhonny Peralta also going deep.
Washington suffered a 2-0 home loss to the Philadelphia Phillies, but it did not cost them as nearest rivals the Atlanta Braves were also beaten, so first place in the NL East was secured
Atlanta slumped 2-1 on the road against the Pittsburgh Pirates, with Starling Marte hitting a home run for the home side, so the Braves will stage the play-off wild-card game on Friday.
The St Louis Cardinals are tidily placed to be their visitors after a 4-2 home success against the Cincinnati Reds, featuring a home run from Jaime Garcia, left them in pole position.
Only the Los Angeles Dodgers can deny St Louis the second wild card from the NL. The Dodgers pinched a 3-2 win against the San Francisco Giants to stay two wins behind with two to play, Elian Herrera singling the decider in the ninth inning to earn a sixth straight win, the best current sequence in the major leagues.
The Chicago Cubs became the second team this season to suffer a 100th defeat, beaten 3-0 by Houston Astros, who were the first to reach the unwanted century mark. Lucas Harrell kept the Cubs scoreless for six innings and Fernando Martinez blasted a home run.
Giancarlo Stanton homered to guide the Miami Marlins to a 3-2 win over the New York Mets, while the Milwaukee Brewers were 5-3 victors over the San Diego Padres with home runs coming from Carlos Gomez, Rickie Weeks and Jonathan Lucroy.
It took a 13th inning to decide the tussle between the Colorado Rockies and the Arizona Diamondbacks. Colorado eventually took the honours, with four runs at the top of the 13th carrying them to a 7-5 win. A mid-inning pitching change by Arizona saw Mike Zagurski take over from Brad Bergesen and he gave up three runs, the third after a wild pitch.
As Detroit enjoyed their AL Central triumph in Kansas City, in the AL East the New York Yankees were thrashing the Boston Red Sox 10-2. The game was effectively over by the end of the second inning as the Yankees treated their home crowd with homers from Robinson Cano, Curtis Granderson, Russell Martin and Mark Teixeira to lead 9-0.
Victory gave New York a one-game lead over the Baltimore Orioles, who ceded top spot after losing 5-3 to the Tampa Bay Rays. Baltimore's journey to St Petersburg was disrupted by smoke filling a galley on their flight, forcing an emergency landing in Jacksonville.
The Chicago White Sox experienced a bittersweet day. There was a grand slam from Dayan Viciedo in their 11-0 win over the Cleveland Indians but their play-off hopes were extinguished by Detroit's win.
There were similar emotions for the Los Angeles Angels, 8-4 winners against the Seattle Mariners but also eliminated from post-season contention.
The Angels were helpless to prevent the Oakland Athletics not only making certain of a post-season berth but also staying in the frame for first place in the AL West by toppling leaders the Texas Rangers 4-3, moving to just one game off the top spot.
Toronto and Minnesota have long given up hopes of reaching the post-season but it made their clash no less competitive as the Blue Jays edged the Twins 6-5 after a 10th inning, Anthony Gose's single proving decisive.