Hardy's deep drive off right-hander David Phelps allowed Manny Machado to trot home from third base and, on a night that combined sharp pitching and numerous missed opportunities for both teams, produced the contest's first run since the sixth inning.
"We had our backs up against the wall," Hardy said. "It was win or go home, and we knew it. It was intense out there, and it was nice to come through there in the 13th."
Game 5 of the AL Division Series will be played on Friday at 5:07 p.m. ET on TBS, with New York's CC Sabathia and Baltimore's Jason Hammel taking the ball with hopes of extending their respective teams' season into the AL Championship Series.
"It's kind of what we've been used to the whole year," Yankees manager Joe Girardi said. "It's been a grind the whole year. You know, it's been a fight to stay ahead of this club the whole year, and it's pretty fitting."
The winner will fight for the AL pennant with the Detroit Tigers, who eliminated the A's in their own Game 5 on Thursday night. This marks the first time in history that all four Division Series matchups have gone the full five games.
"It's playoff baseball, and the games are extremely tight," Girardi said. "Usually, the difference in these games is one hit."
Phelps was in his second inning of relief after being pressed into service once right-hander Joba Chamberlain was bruised on his pitching elbow by Matt Wieters' broken bat in the 11th inning. Machado opened with a double, Hardy followed suit and that was all Baltimore needed.
"I wanted it down in the dirt, so he could roll it over or swing and miss, and I just left it on the plate," Phelps said of Hardy's hit. "Same thing to Machado; I wanted it down and just left it up."
Jim Johnson used his turbo sinker to retire the Yankees in the home half of the 12th, keeping Baltimore's Cinderella season alive and redeeming himself after allowing five ninth-inning runs in Game 1 and blowing a save opportunity in Game 3.
"The baseball gods let you up off the deck if you stay true to the game," Orioles manager Buck Showalter said.
Alex Rodriguez had another rough night, striking out twice and hearing boos before being pinch-hit for by Eric Chavez in the 13th inning, but he was hardly the only struggling member of a Yankees lineup that went 0-for-9 with runners in scoring position and left 10 men on base.
"We're obviously frustrated after having several situations to do some damage," Rodriguez said. "We couldn't get it done tonight. Tomorrow's another day."
Curtis Granderson went 0-for-5 with three strikeouts and has just one hit in 16 ALDS at-bats, having fanned a team-leading nine times. Robinson Cano, Nick Swisher, Russell Martin and Granderson combined to go 0-for-20 in the loss.
"You're not going to go ahead and get balls right down the middle of the plate," Granderson said. "You can't expect anything like that, but you have to go ahead and hit some of their pitches from time to time."
Though he was long gone by the finish, Phil Hughes turned in the Yankees' fourth strong starting pitching performance of the series, limiting the Orioles to one run -- a Nate McLouth homer -- and four hits over 6 2/3 innings.
Making his first playoff start since the decisive Game 6 of the 2010 ALCS, Hughes pitched out of trouble several times, including helping himself by making a nice defensive play to cut down Machado at home plate in the third inning on a fielder's choice.
"I was trying to find myself, command-wise, early," Hughes said. "My fastball was a little bit all over the place, but I was fortunate to escape a couple of jams, which was good, and I kind of felt a little more comfortable as the game wore on."
Boone Logan, David Robertson and Rafael Soriano pitched scoreless relief to send the game into extra innings, but the Yankees couldn't find any of the pixie dust that fueled their memorable Game 3.
"You know what? It's part of the game," said Raul Ibanez, who couldn't repeat Wednesday's magical performance and grounded out as a ninth-inning pinch-hitter. "The only thing we can control is our preparation, our attitude and our mindset for tomorrow's game."
With the season on the line, Joe Saunders held New York to a Cano RBI groundout and three hits over 5 2/3 innings. His grittiest frame was the third, as Jayson Nix stroked a leadoff double and Jeter wore Saunders down with a 13-pitch at-bat before finally striking out.
Saunders recovered to strike out the side and was also helped by a terrific grab in the fifth by McLouth, who crashed into the left-field fence to snare a Nix drive and then doubled up Martin with a throw to first base.
The Yankees threatened in the seventh as second baseman Ryan Flaherty opened the door, dropping a Martin popup, but Jeter struck out looking against former Yankee Luis Ayala.
The Yankees were banging on that same door in the eighth with two on and no outs, but Darren O'Day came on to strike out a mystified A-Rod on four pitches and induced Swisher to sky harmlessly to right field.
"Obviously, I've gotten a look at [O'Day] for a couple days now," Rodriguez said. "I was hoping the result was a little different today, but it wasn't."
So after trading blows with Baltimore all season long, finally one team will definitively call itself victor by the close of Friday's business. The Yankees, strapping their hopes to Sabathia's broad shoulders, expect it will be them.
"It's time to go," Sabathia said. "This is a one-game playoff, and this is what we play for."