Choo sat out the second game as the Jays won 5-3.
Andrus led off the third with his first homer of the ALDS and the first by the Rangers to cut Toronto's lead to 3-2.
Postseason.tv - All ALDS games between the Blue Jays and Rangers are available.
Last fall, Andrus made two of the three Rangers errors in the seventh inning, which ultimately led to Jose Bautista's three-run home run. The Blue Jays moved on to lose to the Kansas City Royals in the American League Championship Series.
Encarnacion had a two-run homer and Martin a solo shot in the first inning for Toronto, which swept a postseason series for the first time.
They'll enter as the favorites to win the American League pennant. The Jays hit.563 (9 for 16) with runners in scoring position in the first two games of the series.
It's over! Canada's Team is heading back to the #ALCS!
If the Rangers win and pull the series to 2-1, Game 4 will be played at the Rogers Centre Tomorrow, Monday, Oct. 10.
All of it came on the heels of Osuna leaving last Tuesday's wild-card game with a sore shoulder, a scary thought for any pitcher. Texas clinched the AL West title with eight games left in the regular season.
Then they pounded Yu Darvish. "When I left it on the plate, they got it".
Texas scored twice in the eighth, including an RBI single by Carlos Gomez that hit reliever Francisco Liriano in the back of the neck.
It was not a great night for pitching, as both starters struggled on the mound.
While the Jays are known for hitting glorious dingers, they scored the final run thanks to getting it done in the baserunning department. They did exactly that for three games.
Gibbons, Martin and crew have good reason to feel sanguine about the way things have turned around.
Bautista's homer and emphatic bat flip in Game 5 was the lasting image from Toronto's ALDS win over the Rangers last season. "You know what? Whether you like it our not, that's the kind of players we have. We all believe in each other", said Texas outfielder Ian Desmond, who drove in two runs but was also thrown out trying to score on a grounder. In the first inning, Sanchez had trouble locating the strike zone and the Rangers managed a run without a hit.
"He couldn't get in a rhythm and get his pitches going", Banister said. "But yeah, it was a battle". "It was a little bit of a buzzkill at the time". Donaldson ripped a double to right-center on the second pitch.
At first pitch, it was overcast with a temperature of 67 degrees, but the game started on time after rain fell overnight and in the early-morning hours at Globe Life Park.
In May, the play started a fight. But Josh Donaldson and company proved this team doesn't need an ace. The out call stood after a replay challenge by the Rangers.
Aaron Sanchez, one of the best pitchers in Major League Baseball, takes the hill for the Blue Jays.
Game 1 of the ALCS is set for Friday.
"It happened to me a year ago and it's not about the errors, it's about losing the game", Andrus said. Jose Bautista worked a full count, but whiffed on a high, 98-mph fastball for the inning's first out.
Information from the Associated Press was used in this report.