Nathan had been successful on a club-record 31 straight save opportunities before giving up four straight hits, including the two home runs, to the four batters he faced. His last blown save was on April 11 against the Mariners, and he is now 33-for-35 on the season.
The Rangers, with the Athletics losing to the Angels, remain three games in front in the AL West with 19 left to play. Their magic number is 17.
"There's no perfection in this game," infielder Michael Young said. "We have one of the best closers in the game. We're looking forward to giving him the ball in the ninth inning again. If we can keep getting the ball to Joe in the ninth inning, we're going to be in great shape."
Nathan was trying to protect a 4-2 lead and was also pitching for the third straight game. He threw a combined 27 pitches on Tuesday and Wednesday while retiring six straight hitters, including three by strikeout. He had also allowed just one run over his past 14 innings going back to the beginning of August.
But Carrera led off the ninth by hitting a 2-1 fastball over the right-field wall for a home run, making it a one-run game. That hardly fazed Nathan.
"I knew I was still fine," Nathan said. "I still had a lead and I was just trying to get outs and break up their momentum. If I could have gotten the next guy out, it might have done that."
He didn't do that. With Young guarding the line at third base, Russ Canzler followed with a single through the left-side hole. That brought Kipnis to the plate, and he smashed a 1-0 fastball into the right-field seats for a two-run home run.
Nathan, trailing 5-4, then gave up a double to Carlos Santana, and manager Ron Washington brought in Koji Uehara. This was the first time this season that Nathan has failed to retire a hitter, and fourth time in his career, the previous one coming on Aug. 30, 2008. This was also only the second time this season that Washington had to pull Nathan from the middle of an inning.
"You always feel the game is over when you hand the ball over to your closer," Washington said. "But there's no closer that's perfect. We want to be in that situation and giving the ball to Joe. It just didn't happen. They just didn't miss the fastballs he threw across the plate."
The Rangers, who scored two runs in the bottom of the eighth to take the 4-2 lead, are 75-2 this season when leading after eight innings.
"Obviously, when guys pitch so many days in a row, it's tougher for them to get it done," Indians manager Manny Acta said. "The stuff was still there. He's got pretty good stuff. It's just that we put together some pretty good at-bats. It felt like that was our game and we had a chance to come back and get it. Fortunately for us, they went after Nathan and were aggressive at the plate. It was a game that we tried to give away the way we played defense and not driving in runners from third with less than two outs."
The Indians were 1-for-10 with runners in scoring position, and all their runs came off home runs. Rangers starter Derek Holland took a 2-0 lead into the sixth, but gave up a two-run home run to Matt LaPorta.
"One pitch ... LaPorta hit a good pitch that was just a little bit up," Holland said. "That's my fault for not shutting them down and keeping them down when I could."
The Rangers almost tied it in the bottom of the ninth when Elvis Andrus hit a two-out triple off the right-field wall. But Indians closer Chris Perez struck out David Murphy on three pitches to end the game.