Santana ripped a double right down the third-base line. It came too quickly for third baseman Jonathan Schoop, who had replaced an injured Manny Machado an inning earlier, to make a play.
Santana's double gave the Tribe the two-run cushion it would need -- the O's hit a solo homer in the bottom half -- to hold on for an 8-7 win before 18,894 at Oriole Park at Camden Yards.
"It was kind of fitting that he got a big hit, because he hit the ball hard twice for outs," Cleveland manager Terry Francona said. "He's been swinging better lately. He's run into some tough luck and instead of hanging his head he went and got us a game-winning hit."
It's the fourth win in a row for the suddenly surging Indians and matches their best streak of the season.
"We're on a winning streak, ain't we?" outfielder Michael Brantley said. "We're moving in the right direction."
Brantley set the table for Cleveland in the top of the 13th. His one-out double left Francona with the decision to bunt with Lonnie Chisenhall and try to move Brantley into scoring position.
The Tribe got the break it needed. Chisenhall's bunt popped into the air and fell between the first and second basemen for a single. Relief pitcher Troy Patton walked the next batter and suddenly the bases were loaded with one out for Santana.
"He's getting a couple counts in his favor and just hasn't been able to finish the at-bat off," Baltimore manager Buck Showalter said. "He's got some things that he's capable of that he's just not executing."
Santana's double ultimately saved more than just a victory for the Indians, but potentially an entire weekend of complications. Cleveland's bullpen has pitched 18 1/3 of the 26 innings in the past two days and the Tribe had to call up a pair of pitchers before Thursday's game as reinforcements. Just two hours before the game, Francona wasn't even quite sure just who would be available.
Had the game gone much longer, there was also the possibility that Friday's starter T.J. House would have had to pitch on Thursday.
"You don't really expect that," said Josh Outman, who pitched two scoreless relief innings for the Indians and got the win. "You'd like to get a win in regulation, but it's the best thing for this team right now that we were able to grind through the last two days and pull wins out both times."
Cleveland was forced to use six more pitchers on Thursday after starting pitcher Justin Masterson unraveled in the sixth inning. He delivered five shutout frames to start the game, but surrendered five runs in the sixth to set up the back-and-forth contest that spanned the remainder of regulation.
The O's took a two-run lead after that sixth inning, but the Tribe immediately responded with two runs in the top of the seventh to even the score. In the bottom half, the Orioles took a one-run lead, but the Indians responded with a pinch-hit home run from Chisenhall to send the game into extras.
With Cleveland on perhaps its most impressive winning streak of the season, Francona is starting to see shades of last year's team in this year's iteration. In 2013, the Tribe made a habit of winning close, nerve-racking wins. With three extra-inning wins as the backbone of this streak, the Indians are finding their identity.
"We're becoming the team that we want to be and that doesn't mean that we're going to win every game," Francona said. "We're going to still make mistakes, but there's not a better feeling as a staff, manager, coaches than when you love your team."