Lindor, who struck out with the winning run at second base in the ninth in a loss on Tuesday, drove the first pitch from Trevor Hildenberger (2-3) over the wall in right to trigger a wild celebration.
The All-Star shortstop skipped around the bases before being mobbed at home plate by his teammates.
Cleveland's dependable closer -- and career saves leader -- not only let the lead go, but he cost Indians starter Mike Clevinger his first win since July 1. The right-hander limited the Twins to one run and five hits over seven strong innings, retiring the final 11 batters he faced before turning things over to the Indians' rejuvenated bullpen.
However, Allen's 2-1 knuckle curve didn't fool Sano, as Minnesota's cleanup hitter pounded his eighth homer over the wall. It was the ninth homer allowed by Allen in 47 1/3 innings -- a concerning statistic for the Indians as the push toward the playoffs.
Minnesota committed three errors in the first six innings.
The Indians didn't do much against Twins starter Jake Odorizzi, but they managed to scratch out a run in the fifth to take a 2-1 lead.
Gomes and Guyer opened with singles, and following a force out that put runners at the corners, Michael Brantley hit a slow grounder to short to give Clevinger a thin cushion.
Twins center fielder Jake Cave helped the Indians take a 1-0 lead in the first with a pair of miscues -- one mental, one physical.
Lindor led off with a shot that Cave broke in on before realizing the ball was hit harder and it sailed over his head for a double. Brantley followed with a sinking linger that Cave charged but dropped for an error. One out later, Lindor scored on Edwin Encarnacion's fly to Cave, whose throw to the plate was way offline.