Carlos Carrasco (16-6) pitched into the seventh inning to get the win.
With the win, Cleveland would clinch their second consecutive American League Central Division title if Minnesota loses to Toronto on Saturday night.
Jason Hammel (8-12) gave up seven runs (six earned) and 11 hits in six innings in taking the loss.
The Indians took a 1-0 lead in the second inning on a sacrifice fly by Abraham Almonte. The lead didn't last very long, however, as Alex Gordon homered in the top of the third for a 1-1 tie.
Cleveland sent seven men to the plate in the third inning and two of them scored, on an RBI single by Carlos Santana and a sacrifice fly by Encarnacion, giving Cleveland a 3-1 lead.
Kansas City got a run back in the fourth, which began with a double down the right-field line by Melky Cabrera. A wild pitch by Carrasco allowed Cabrera to move to third, and he scored on a sacrifice fly by Brandon Moss to cut the Cleveland lead to 3-2.
The Indians blew it open with a four-run sixth inning. Yandy Diaz and Almonte led off with singles, putting runners at first and second. Hammel retired the next two batters, but Lindor bounced a double off the left field wall, driving in both runners to make it 6-2.
It's the 10th consecutive game in which Lindor has had an extra-base hit, which is a team record.
Austin Jackson then singled and Lindor slid home ahead of the throw from center fielder Lorenzo Cain. Jackson attempted to advance to second on the throw home, and catcher Drew Butera threw wildly to second for an error. The ball rolled back into the outfield to Cain, allowing Jackson to score to extend the lead to 7-2.
In the top of the seventh, Butera and Whit Merrifield had two consecutive two-out, two-strike RBI hits to cut the margin to 7-4 before reliever Andrew Miller relieved Carrasco and got the third out.
Encarnacion's home run came leading off the seventh inning against reliever Kevin McCarthy.
NOTES: Indians 2B Jose Ramirez did not play Saturday and may not play Sunday due to a sore hamstring. ... Indians OF Brandon Guyer is sidelined with an aggravated right wrist. He is expected to be unavailable for five to seven days, and won't accompany the Indians on their six-game trip to Anaheim and Seattle that begins Tuesday... . Indians 2B Jason Kipnis will be activated off the disabled list and will make his debut in center field on Sunday. Kipnis, a center fielder in college at Arizona State, is being given a trial as a replacement for OF Bradley Zimmer, who is out for the year with a broken right hand... . LHP Danny Duffy will be activated off the disabled list and will start Sunday for the Royals. Duffy has been on the DL for three weeks with a left elbow impingement... Royals 1B Eric Hosmer has 180 hits, eight shy of his career high of 188, set in 2013.