The Tribe remained unfazed through it all, and snatched a 3-2 extra-inning win over the Royals at Kauffman Stadium.
"That was one of the funner games to be a part of, it certainly helps when you win," Indians manager Terry Francona said. "There was so much that was going on and not a lot of scoring though. They had baserunners it seemed like every inning, and we found ways to wiggle out of a few."
Michael Brantley delivered the game-winning hit in the 11th, when he chopped a single over a drawn-in Kansas City infield, scoring Jose Ramirez, who ignited the rally with a leadoff triple.
Ramirez took an extra base on what looked like a routine double.
"I [just] about swallowed my tobacco when he rounded second. But he made it," Francona said. "You were going to have to lasso him to stop him."
Carlos Santana padded the lead with an RBI single.
The Royals threatened in the bottom half of the frame. Salvador Perez drove in Jarrod Dyson, but was left stranded after Josh Tomlin struck out Erik Kratz.
Tomlin was the seventh reliever Francona used, and he gutted through two innings after finishing off Friday's 6-1 win.
"He means so much to that group out there, he was wiped out, but he was going to figure it out," Francona said.
Cleveland's second straight win over the Royals closed the gap to 3 1/2 games in the American League Central with the finale of the series coming Sunday. Kansas City dropped into a tie for first place with the Tigers in the American League Central.
Yan Gomes drove in the Indians' first run with an RBI double off Royals starter James Shields in the fourth inning. Gomes returned from the seven-day concussion disabled list just one day earlier.
Kansas City tied the game in the eighth inning on a fielder's choice by Lorenzo Cain. But they squandered myriad opportunities in the last four innings.
"We weren't getting any hits with runners in scoring position. It was plain and simple," said Royals manager Ned Yost, whose team went 2-for-18 with runners in scoring position. "We had a multitude of opportunities starting in the first inning, we just couldn't take advantage of it."
Trevor Bauer twirled 5 2/3 scoreless innings, registering his second straight zero-run outing, a career first for Bauer.
An even more impressive feat was the first-inning jam he escaped.
Bauer allowed the first three runners to reach for a bases-loaded, no-out conundrum. This looked ominous at the time, particularly considering he has allowed 16 runs in the first inning this season, five more than any other frame.
But Bauer struck out the next two batters to bring up Raul Ibanez.
"Early innings for me are tough and so I was fired up just being able to get to that position, to get two outs and have a chance of getting out of it," Bauer said.
He got ahead of Ibanez, 1-2, then bounced a slider in an attempt to get him to chase. Ibanez checked his swing, ruled third-base umpire Bill Welke, which prompted an argument from pitching coach Mickey Callaway, who was ejected.
Bauer ignored the drama and struck out Ibanez four pitches later, ending the threat.
"The way the rest of the game went, turned out to be a really big inning to get out of that with giving up none," Bauer said. "Usually in a situation like that, you try to give up just one or two, just don't let it be a big inning."
Cleveland got on the board when Jason Kipnis and Gomes whacked back-to-back doubles in the fourth inning.
The seven relievers combined to toss 5 1/3 innings, allowing two runs (one earned).
"Down the list, everyone did exactly what they're supposed to do," Bauer said.