The club confirmed Mills, in his third season as manager, hitting coach Mike Barnett and first base coach Bobby Meacham were leaving after their Major League record worsened to 39 wins and 82 losses with their latest setback. An interim manager is expected to be announced later today.
A nine-run fifth inning highlighted by Aaron Hill's three-run jack means the Astros will be on the wrong end of a 6-0 clean sweep if they lose their next meeting at Minute Maid Park.
Elsewhere, Jon Niese matched zeros with Edwin Jackson through six before Ike Davis broke the tie with a two-run homer in the seventh as the New York Mets downed the Washington Nationals 2-0.
Jon Lester delivered his second convincing win in as many starts for the Boston Red Sox as they defeated the New York Yankees 4-1.
Joaquin Arias drove in three runs to help the San Francisco Giants outlast the San Diego Padres 8-7, while Bartolo Colon pitched an impressive eight innings in the Oakland Athletics' 8-5 victory over the Cleveland Indians.
John Jaso came off the bench and hit a walk-off, bases-loaded sacrifice fly as the Seattle Mariners beat the Minnesota Twins 3-2.
Starlin Castro came within a homer of the cycle, and the Chicago Cubs won a slugfest over the Cincinnati Reds in the second game of their twin bill. The 9-7 success followed a 5-3 setback.
Giancarlo Stanton belted a three-run homer in a four-run first inning as the Miami Marlins saw off the Colorado Rockies 6-5, while the Philadelphia Phillies defeated the Milwaukee Brewers 4-3.
The St Louis Cardinals moved a game behind the Pittsburgh Pirates in the NL Central standings and wild card race with a 5-4 success.
The LA Dodgers beat the Atlanta Braves 6-2, the Kansas City Royals defeated the Chicago White Sox 9-4, the Baltimore Orioles saw off the Detroit Tigers 3-2 and the Texas Rangers beat the Toronto Blue Jays 2-1.
The Tampa Bay Rays trailed the LA Angels 8-0 after three but a 7-0 fifth innings paved the way for a stunning comeback by the visitors, who won 10-8 in the night's final match to finish.