Devon Travis hit a one-out single, before advancing to third base on a single by Donaldson. That set the stage for Encarnacion, who hit a three-run homer off of Ubaldo Jimenez to win the game for the Blue Jays.
After Blue Jays closer Roberto Osuna left the top half with an apparent injury, reliever Darren O'Day did the job for Orioles in the bottom half, pitching a scoreless frame to send it to the 11th.
The Blue Jays couldn't cash in on a leadoff double from Josh Donaldson. After Edwin Encarnacion took an intentional walk, Jose Bautista struck out and Russell Martin hit into an inning-ending double play.
Niether side could gain an advantage, prompting a showdown in the ninth inning. The Orioles went down 1-2-3 in the top half, and the Blue Jays did the same, with Kevin Pillar striking out before Carrera singled and Devon Travis grounded into an inning-ending double play.
A fan threw a beer car at Orioles left-fielder Hyun-soo Kim as he tracked the third out of the inning, a fly ball at the warning track. The incident prompted Baltimore manager Buck Showalter to have a lengthy discussion with the umpiring crew.
Stroman came out for his final inning of work, and retired Trumbo, who had homered earlier in the contest.
Fifth inning - Jays tie it up 2-2
After a scoreless top half, Michael Saunders slices a one-out ground-rule double to left field, before moving to third on a double from Kevin Pillar. Carrera's single brought Saunders home to tie the game 2-2.
Fourth inning - Orioles go up one run, lead 2-1
The heavy-hitting Mark Trumbo puts Baltimore up a run with a two-run shot, prompting the Blue Jays to warm up releiver Joe Biagini.
Stroman throws another perfect inning with two strikeouts; for the third out, J.J. Hardy lunges weakly at an 0-2 offering that is well off the plate. Tillman regroups nicely for the Orioles, retiring the Blue Jays on a groundout, a strikeout, and a meekly stroked fly ball to right.
Second inning - Blue Jays take lead
Ezequiel Carrera, starting in left field for Toronto, makes a nice running grab in foul territory on a long fly off the bat of Matt Wieters. Stroman then does a bit of a strut off the mound after striking out Chris Davis on a nasty slider for the third Baltimore out.
Jose Bautista increases the excitement level by stroking a 3-1 Tillman pitch deep to left for a home run, giving the Blue Jays a 1-0 lead. Bautista, all business, quickly rounds the bases while fans twirl their rally towels in the stands.
The decibel level inside Rogers Centre is almost otherworldly as Toronto starter Marcus Stroman takes the mound, and it gets even louder when Baltimore leadoff hitter Adam Jones flies out to centre on the first pitch. Stroman retires the side in order on 12 pitches. Baltimore starter Chris Tillman, doing his best to ignore the catcalls from the stands, also needs just 12 throws to mow down the first three Blue Jays batters.
Baseball fans rejoiced. The retractable roof at Rogers Centre was open for Tuesday evening's game.
The one-game elimination might as well come down to a coin flip. Calling the Battle of the Birds is next to impossible – a cursory look at the numbers suggests neither team holds clear advantage over the other. The Blue Jays earned the right to host the game by winning more games against the Orioles in the regular season 10-9.
So it's anybody's guess who will advance to the AL Division Series against the league's top team, the Texas Rangers.
Hitting: Both Toronto and Baltimore are proficient at hitting the long ball, but the Orioles showed exceptional power this season. Baltimore hit an MLB-best 253 regular-season home runs, while Toronto's 221 was fourth in the Major Leagues.
Orioles sluggers Chris Davis and Adam Jones historically hammer more homers against the Blue Jays than any other team. Davis has hit 35 in 110 games against the Blue Jays (four in 2016) while Jones has 32 in 155 career games against Toronto (three in 2016).
Toronto, no slouch on offence, had a slight edge in total runs over 162 games, scoring 759 to Baltimore's 744.
The Blue Jays, with maybe the most star-studded lineup in baseball, will lean on the bats of reigning AL MVP Josh Donaldson, heavy-hitting DH Edwin Encarnacion and Jose Bautista, to name a few.
In terms of going head-to-head, the Blue Jays had more success against Orioles' pitchers than any other of their AL East division rivals, each of which they faced 19 times this season. Toronto scored 97 runs, an average of 5.10 per game, against Baltimore in the regular season.
The Orioles, meanwhile, plated 81 against Blue Jays pitching.
Pitching: As starting pitching goes, regular-season stats suggest the Blue Jays have a clear advantage with their AL-best 3.64 rotation earned-run average. But in a one-game elimination, those year-long numbers go out the window.
Frank Gunn-Fred Lum/The Canadian Press-The Globe and Mail
Chris Tillman will start for the Orioles and Marcus Stroman will go for the Blue Jays.
Tillman (16-6, 3.77 ERA, 1.28 WHIP): Historically he's been awful against the Blue Jays, but Tillman turned things around in 2016. The right-hander is 5-10 with a 5.44 ERA for his career against Toronto, but this season was 1-0 with a 3.63 ERA in four starts (22.1 innings).
Stroman (9-10, 4.37 ERA, 1.28 WHIP): He has not had great success against the Orioles throughout his career, putting up a 2-3 record with a 5.27 ERA in seven games (41 innings). This season, he's 1-2 with a 7.04 ERA in four games.
Despite a difficult 2016, Stroman has been strong in 11 starts since Aug. 1, posting a 3.28 ERA.
As the Globe's Robert MacLeod writes, Stoman's struggles have not undermined his confidence and bravado.
"It's my personality," the 25-year-old said following a Blue Jays workout at Rogers Centre on Monday. "It's the individual I am. I pitch with a lot of emotion, lot of energy."
Baltimore's bullpen: Orioles relievers were the best in the AL this season, posting a collective ERA of 3.40. Their biggest asset is the late-innings combinations of Mychal Givens, Brad Brach, Darren O'Day and closer Zach Britton, a lethal set-up-shutdown option.
Britton in particular has been outstanding, converting on 47 of his 47 save opportunities, making him a candidate for the AL Cy Young award, a rarity for relief pitchers.
Blue Jays bullpen: The much-maligned Blue Jays relief staff, which had a 4.11 regular-season ERA, is led by 21-year-old Roberto Osuna, the team's closer the past two years. Osuna has struggled in the back half of the season, but that hasn't stopped the Jays from riding him. Osuna (36 saves, 2.68 ERA) pitched two innings on Saturday and another one on Sunday in Toronto wins over the Red Sox.
Where to watch: As of Monday at noon, the ticket resale site Stubhub had approximately 4,000 tickets for sale for Tuesday evening game, starting as low as $80 (U.S.) for 500-level seats.
But if you can't snag a ticket, fans can head downtown to watch the game on a big screen downtown at Nathan Phillips Square.
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