According to Sizemore, it was the first inside-the-park homer of his life. The speedy outfielder, a former star football player, said he never got one even in Little League.
It also gave him the first two-homer game of his big-league career and 90 extra-base hits this season, the most in baseball.
Sizemore (.292) also leads the majors with 131, to go with career highs of 52 doubles and 27 homers along with 11 triples, which ties his previous best.
His inside-the-park homer came on a bloop to the opposite field that Rangers left fielder Carlos Lee made an awkward attempt to catch with a poorly timed slide. The ball rolled all the way to the wall as Sizemore circled the bases.
"It's usually those first two or three steps out of the box that give you a chance to do it or not," manager Eric Wedge told reporters. "He was getting after it like he always does. With the way the ball bounced, he was able to get it."
Sizemore's heroics overshadowed a good game by Aaron Boone (.251), who went 2-for-5 with four RBI and two of Cleveland's four stolen bases.
Jake Westbrook (14-10) worked five innings for the win, allowing nine hits and five runs, but benefitting from the Indians' 12-hit attack and solid relief work.
Brian Sikorski struck out three and allowed one run over 2 2/3 innings. Juan Lara gave up one hit and got one out and Jason Davis allowed one hit in a scoreless ninth.
Shin-Soo Choo (.277), Franklin Gutierrez (.286) and Joe Inglett (.287) also had two his apiece for Cleveland.
The Indians didn't make an error for the second straight game, but did strike out 10 more times, led by Boone, Gutierrez and Victor Martinez with two apiece.