Hannahan led off the frame with a high fly that ricocheted off the top of the wall in right field, just inside the foul pole. The ball caromed past Texas' Nelson Cruz and back toward the infield, and Hannahan sprinted to third base for an apparent triple.
Skipper Manny Acta then asked home-plate umpire Dale Scott to review the play. Scott convened with the rest of his crew, and after a delay of two minutes and 20 seconds, Scott ruled the play a home run, Hannahan's second of the season.
The long ball gave Cleveland a two-run lead. Shin-Soo Choo provided the first two tallies with a two-run homer in the second inning.
"It was nice to see Choo come alive and hit that homer, and Jack continues to be big for us," Acta said.
Hannahan notched a pair of hits to raise his average to a team-best .306. He ranks second on the club in RBIs, with 16.
The Indians collected 10 hits, all off Rangers starter Colby Lewis.
"We laid off some tough pitches and guys didn't try to do too much," Acta said. "Choo hit the homer to dead center; he wasn't trying to yank the ball. Everyone had a good approach. We hit a few balls up the middle. He pitched well, but we scored enough to hand it to our bullpen."