"That Escobar can hit and we've known it since the first time we saw him," Braves manager Bobby Cox said.
Escobar went 2-for-5 and is batting .327.
Cleveland's Casey Blake extended his hitting streak to 24 games with a tiebreaking homer in the eighth, but Sabathia (10-2) couldn't make it stand up.
"Tonight's all on my shoulders," Sabathia said, still wearing his sweat-soaked uniform in a somber Indians clubhouse. "I take all the blame. I'm disappointed. Casey had the big home run and everyone was fired up."
Indians manager Eric Wedge said he didn't consider lifting Sabathia after eight innings since closer Joe Borowski had pitched in each of the previous two games.
"With the way C.C. pitched in the seventh and eighth, he was our guy," Wedge said. "We didn't make a play. There are other things that go into it."
Sabathia had retired eight straight before yielding a leadoff double to Jarrod Saltalamacchia in the ninth -- Atlanta's first extra-base hit after 10 singles.
Pete Orr pinch ran, but did not advance when Brian McCann grounded to shortstop Jhonny Peralta, who misplayed the ball for an error. Chris Woodward bunted both runners over and Escobar lined a shot over the head of left fielder David Dellucci, who couldn't make a leaping catch near the warning track.
"Escy's a clutch player," Saltalamacchia said. "Every time in that situation, he's going to make something happen.
"When I saw C.C. come back out for the ninth, I had a good feeling that we were going to do something. I just felt it."
Rafael Soriano (2-0) yielded Blake's 10th homer in one inning of work, but got the win.
Bob Wickman allowed two baserunners in the ninth but got his 12th save in 15 chances. It was his first appearance against his former team since being traded to the Braves on July 20.
The right-hander gave up a single, walk and committed a balk, but got three strikeouts as he bounced back from yielding three runs Thursday night to blow the save in a 3-2 loss at Minnesota.
"We had (Johan) Santana beat and had it get away," Cox said. "Tonight, we kept battling against another great lefty and won it."
The Braves won for the fourth time in 13 games, improving to 2-6 in interleague play this season and 13-23 over the last three years. It was their first win in Cleveland since Game 4 of the Braves' six-game triumph in the 1995 World Series -- when Escobar was a schoolboy in his native Cuba.
The Indians fell to 21-9 at home with the fifth loss in their last seven games at Jacobs Field.
The Braves battled back from a 3-0 deficit by accumulating seven singles of all shapes and sizes in the fifth and sixth innings.
Woodward's RBI single in the fifth made it 3-1 -- the first run allowed by Sabathia in 22 1/3 innings, dating back to May 31.
Singles by Chipper Jones, Andrew Jones and Jeff Francoeur made it 3-2 in the sixth. Matt Diaz added another single when Blake at third couldn't quite reach his popped-up bunt, loading the bases. McCann's sacrifice fly tied it at 3.
Sabathia allowed four runs and a season-high 12 hits in 8 1/3 innings. It was the most hits he allowed since July 15 of last year against Minnesota, when he gave up 13.
The Indians made it 3-0 in the fourth. Martinez and Travis Hafner singled and Peralta reached when Escobar misplayed his grounder for an error, loading the bases.
Carlyle allowed two earned runs and six hits over six innings in his fourth start and fifth appearance this season for Atlanta.
- Diaz went 3-for-4 and his hitting .385 (10-for-26) during a six-game hitting streak.
- Soriano has allowed runs in only four of his 30 appearances this season.
- Sizemore's steal was his 20th, two shy of his career high, set in 2005 and matched last season.