The Royals split their series against the Cleveland Indians while the Chicago White Sox upset the Tigers on Monday.
It saw the Tigers' lead atop the American League (AL) Central standings cut to just a game late in the season.
Lonnie Chisenhall hit a two-run double in the 10th as the Indians beat the Royals 4-3, completing the game suspended on August 31.
But Danny Duffy led the Royals to a 2-0 win in the second game of the day between the teams, pitching six shutout innings.
Chris Bassitt pitched almost eight scoreless innings for his first MLB win as the White Sox edged the Tigers.
Central is the only division still up for grabs in the AL.
The Oakland Athletics, who had an 8-4 win over West champions the Los Angeles Angels, and the Royals sit in the wildcard places.
The Seattle Mariners are two games behind and were crushed 14-4 by the Toronto Blue Jays, who are almost eliminated.
The Indians sit 3.5 games behind the wildcard.
Derek Jeter had three RBIs as the New York Yankees – four games behind in the wildcard race – enjoyed a 5-0 win over East champions the Baltimore Orioles.
In the National League (NL), the Pittsburgh Pirates closed in on a play-off spot as Andrew McCutchen hit a solo homer in the sixth in a 1-0 win over the Atlanta Braves.
The San Francisco Giants closed the gap on NL West leaders the Los Angeles Dodgers to 3.5 games with a 5-2 win through 13 innings.
NL Central leaders the St Louis Cardinals beat the Chicago Cubs 8-0 as pitcher Adam Wainwright picked up his 20th win.
In other matches, the Texas Rangers edged the Houston Astros 4-3, the Arizona Diamondbacks were 6-2 winners over the Minnesota Twins and the San Diego Padres beat the Colorado Rockies 1-0.