Detroit swept the best-of-three American League wild card series to reach a second-round matchup against the Cleveland Guardians, who host the opener on Saturday.
The Kansas City Royals also advanced, edging the Orioles 2-1 in Baltimore for a two-game sweep in their AL series.
In National League action, the San Diego Padres held off the Atlanta Braves 5-4 to advance, but the Milwaukee Brewers rallied with three runs in the eighth inning for a 5-3 victory over the New York Mets to force a decisive game three on Thursday.
The Brewers' 20-year-old rookie Jackson Chourio led off the eighth inning with his second home run of the game, an opposite-field shot off Phil Maton that pulled the hosts level at 3-3.
Garrett Mitchell followed with a two-run blast that put the Brewers up 5-3 and relief pitcher Devin Williams retired three straight Mets batters to close out the win.
Chourio, who led off the bottom of the first with a home run, became the second-youngest player to have a multi-homer game in the play-offs. Andruw Jones was 19 when he homered twice in game one of the 1996 World Series.
The upstart Tigers, who had not reached the play-offs since 2014 and had not won a play-off series since 2013, ousted an Astros club that had reached the AL championship series in each of the past seven seasons.
With the contest deadlocked and the bases loaded, Ibanez blasted the game-winning hit down the left-field line off left-handed Houston relief pitcher Josh Hader.
"I think that was the best at-bat of my life," Ibanez, a 31-year-old Cuban, said through a translator.
'Not done yet'
The Royals, in the play-offs for the first time since winning the World Series in 2015, will face the New York Yankees in the second round.
"This group is special. We're not done yet," said Royals shortstop Bobby Witt Jr., who drove in the winning run for the second game in a row.
The Orioles lost their 10th consecutive play-off game. They haven't won a play-off series since 2014.
In San Diego, the Padres scored five runs with two outs in the second inning and made the lead stand up to book a second-round clash with Shohei Ohtani and the Los Angeles Dodgers.
Kyle Higashioka homered to start the burst. Three Padres batters hit singles before Manny Machado hit a two-run double and Jackson Merrill smacked a two-run triple as San Diego took a 5-1 lead.
Jorge Soler homered in the fifth for Atlanta, and Michael Harris II belted a two-run homer in the eighth before the Padres polished it off.
When Higashioka caught Travis D'Arnaud's pop-up foul for the final out, Padres fans began chanting "Beat LA!"
It will be the third time in five years that the National League West division rivals will play in the NL Division Series.
"This is what everyone wanted," Machado said of the match-up with the Dodgers.
"And, you know, it's been a hell of a year for both teams going back and forth. It's going to be an exciting series for us to go out there and play the Dodgers."
