CHICAGO — Joe Maddon didn’t exactly ease the minds of a jittery Cubs fan base, many of whom emotionally found themselves plunged into despair familiar from the bad old days.

“Please be nervous. Absolutely, you should be nervous,” Maddon said Sunday, a few hours before the Cubs tried to stave off elimination in Game 5 of the World Series. “We have to win tonight, so go ahead and be nervous. It’s up to us to get you beyond that moment and get back to Cleveland.”

The ensuing white-knuckler of a game didn’t do much for those nerves, but the Cubs will play on. They received a solid outing by Jon Lester, just enough offense and an occasionally wobbly eight-out save by Aroldis Chapman in a 3-2 victory over the Indians in front of a loud gathering of 41,711 at Wrigley Field that rarely sat down.

The Indians, trying to win their first title since 1948, lead the series 3-2, with Game 6 on Tuesday night at Progressive Field. The Cubs have not won a World Series since 1908.

“We’re still here, right?” leadoff man Dexter Fowler said. “It’s win or go home. We’ve got two more, we’ve got to win both of them or we’re going home. We’re excited. We’re up for the challenge.”

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After Chapman, called on to pitch a career-high 2 2⁄3 innings, struck out Jose Ramirez with a 101-mph fastball to end the game, the crowd erupted. Cubs fans were able to celebrate a World Series home victory for the first time since 1945, the last time the franchise made it.

“We’re enjoying this win. It’s nice to give these fans something to cheer for. It was nice to hear ‘Go Cubs Go’ after the game,” catcher David Ross said of the song all of Wrigley sings after a victory. “We’re excited about getting back to Cleveland.”

Lester, who took the loss in Game 1, allowed two runs and four hits in six innings in Game 5. One of the runs came on a second-inning home run by Ramirez that gave the Indians a 1-0 lead.

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With the Cubs leading 3-2, Carl Edwards Jr. allowed a leadoff single by Mike Napoli in the seventh, and a passed ball sent him to second before Carlos Santana flied out. Maddon, showing the desperation born of an elimination game, then brought in Chapman.

Ramirez struck out swinging on a 101-mph fastball, and after Chapman hit Brandon Guyer, he got Roberto Perez to ground to second to end the threat.

Rajai Davis reached base on an infield single when Chapman failed to cover first in the eighth, then stole second with one out and third with two outs. But Chapman, acquired from the Yankees before the Aug. 1 trade deadline, retired the red-hot Francisco Lindor on a called third strike for the third out and pitched a perfect ninth.

“There’s all kinds of drama out there,” Maddon said, not understating the evening in the least. “When you have a guy like that that can pitch that many significant outs in the latter part of the game, it’s pretty cool.”

Lester walked two in a two-run first inning in Game 1 but was sharp from the start Sunday night, striking out the side on 13 pitches.

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Cleveland righthander Trevor Bauer was better than he had been in the Indians’ 5-1 loss in Game 2, but he didn’t go deep, allowing three runs and six hits with seven strikeouts in four innings. All of the runs came in the fourth.

With the Indians leading 1-0, Kris Bryant — who was 1-for-14 in the first four games — led off by ripping a 1-and-1 pitch to left for a tying home run. Anthony Rizzo doubled off the rightfield wall and Ben Zobrist singled to center to put runners at the corners with none out.

Addison Russell’s dribbler to third went for an infield single and a 2-1 Chicago lead. Bauer struck out Jason Heyward, but Javier Baez bunted for a single to load the bases and Ross’ sacrifice fly to left made it 3-1.

Davis singled with one out in the sixth and stole second, and Lindor’s two-out RBI single made it 3-2. But Ross threw out Lindor trying to steal second to end the inning.

“You know, that’s pretty impressive,” Indians manager Terry Francona — who fell to 11-2 in World Series games — said of the Cubs’ pitching overall. “Sometimes you’ve got to respect what the other team can do, too. Sometimes they beat you. I didn’t think we beat ourselves. I thought they beat us.”