Chisenhall and Swisher took full advantage of still being on offense in the fifth.
"In that situation right there, huge knock by [Chisenhall] to be able to tie the game up and just continue to keep that inning going," Swisher said. "And then to be able to come up and hit that two-run home run to put us up [was great]. Obviously, any time we have a chance to strike or to, what we call, gas pedal a little bit, we want to do that."
The Tribe (46-46) snapped a four-game losing streak against the White Sox while also climbing back to .500 for the first time since June 20. Swisher finished the game 2-for-4 in his third multihit performance of the last 10 games, and he is 11-for-37 with three homers since July 1.
"I think he's certainly doing much better," Tribe manager Terry Francona said. "It just wouldn't shock me if you look up and somehow, maybe his batting average won't be what he is career-wise, but it wouldn't surprise me if you look up and see the home runs and RBIs. Guys have a way of doing that."
Tribe starter Corey Kluber fought to overcome shaky command through the early stages of the game but pitched well enough to earn his ninth win of the season with some help from the offense. The right-hander allowed four earned runs -- the first time he's surrendered that many in his past seven outings -- in a six-inning start that saw him scatter eight hits and strike out five.
"Location wasn't that great, but the important thing was that we got a win," Kluber said. "[The offense] would bounce right back, score and answer."
The White Sox offense struck first, slapping three straight hits off Kluber in the second inning to put the Indians in a two-run hole. David Murphy provided the quick answer on a two-run homer -- his first time going yard since May 21 -- to even the score.
The two clubs went on to trade lone runs in the fourth inning. The White Sox plated one courtesy of Adam Eaton, who doubled a screamer to the gap that carried just beyond the reach of Michael Brantley. The Indians threatened later that inning by loading the bases with two outs, and recent acquisition Corey Dickerson did his part by drawing a walk that tied the game for a second time.
"We kept answering back, and we had to for a while," Francona said. "We did a really good job of swinging at strikes, Murphy got a good pitch to hit, Swish got a pitch to hit, some two-out hits. We gave ourselves more than one or two opportunities tonight."
Adam Dunn gave the White Sox yet another slim lead in the fifth on a solo shot that barely managed to work its way beyond the wall in center field. That, however, would mark the end of any scoring from the South Siders, who were held hitless over the final four innings.
Relievers John Axford, Bryan Shaw and Cody Allen combined to put up zeros the rest of the way, giving the Cleveland bullpen a collective 0.34 ERA over its last 26 1/3 innings.
"The bullpen came in and shut them down," Kluber said.
In what has been a trying season for Swisher, the first baseman has finally been able to smile about his hitting lately. And on the same day that LeBron James announced his homecoming to northeast Ohio, Swisher would be allowed to join in on the celebration.
"I almost felt like I should take some powder and just throw it up in the air," Swisher said.