Cleveland exceeded its combined run total in the final two games of its just-concluded series against the Royals in the first three innings of this blowout.
With one out in the first, Nick Swisher hit his 18th homer, a solo shot to left-center. Jason Kipnis followed with a single and Carlos Santana walked to set the table for Raburn, who ripped a 1-2 fastball from White Sox starter John Danks into the left-field seats for his 16th homer, staking Kluber to a four-run lead.
Danks said he couldn't get anything to work for him.
"I just couldn't do what I wanted to do," the left-hander said. "Nothing worked. I threw the ball where I wasn't supposed to throw it and got my [butt] kicked."
Raburn -- who went on the disabled list in August with a strained left Achilles and had pain in the heel flare up again Saturday -- has hit 17 career home runs against the White Sox, the most he has hit against any team.
"We said coming into this series that Raburn would hopefully play a big part, because we were going to face three lefties," manager Terry Francona said. "But he did what he's done so often this year. He not only gets hits, but he gives us a lot of production for a guy that plays maybe half the year or not even [half]. He's given us a lot of production out of that bat."
Francona added that Raburn's confidence and ability to keep his swing consistent, despite having played in only three games since Aug. 18 due to calf and heel injuries, has enabled him to continue to produce offensively.
"I think he's confident, and he should be," Francona said. "He's had success all year and I think confidence plays a big part in it. But he's maintained his swing all year. It's been pretty rare where he's not had his timing or not had his balance. He's really been consistent with it and as a bench player, that's not the easiest thing to do."
After adding one run in each of the next three frames, Cleveland posted a seven-run fifth inning that included a 17-minute rain delay.
Asdrubal Cabrera launched a solo shot for his 12th homer, and following three consecutive walks, Michael Bourn and Swisher hit back-to-back singles. Following another walk, Santana also singled before Raburn hit a two-run single to make it 14-2.
Kluber, making his second start since a right middle finger sprain sidelined him for a month, allowed a solo homer to Paul Konerko in the second and an RBI single to Alejandro De Aza in the third.
"I thought early [Kluber] was fighting [his command]," Francona said. "[He was] kind of in and out of the zone. I thought when we scored and we spread it out a little bit, I thought he kind of got back in sync, [and] even with the rain, I thought he held his stuff pretty well."
Chicago tacked on a run on a sacrifice fly against reliever Vinnie Pestano in the eighth.
Kluber allowed six hits, walked one and struck out two in five innings. He has walked one batter or fewer in five consecutive starts. He is 5-1 with a 2.33 ERA (15 earned runs in 58 innings) in nine starts following an Indians loss, again proving to be a stopper Thursday after Cleveland's two losses to Kansas City in its last series.
Kluber has yielded three earned runs or fewer in seven of his last eight starts dating back to July 7.
"I was a little sloppy to start out with," Kluber said. "I didn't have my best command early on, but the nice part about that is that the offense came out and put up a lot of runs. … I think I was kind of inconsistent with my delivery early on and I wasn't getting my arm in a good slot, pitch after pitch. But, I kind of figured it out a little bit just playing catch during the delay and [pitched better after that]."
The Indians have won 12 of 14 games this season against the White Sox, outscoring Chicago 88-48 in the process. Cleveland has also won a franchise-record nine in a row against the White Sox, as well as seven of the eight games they have played at U.S. Cellular Field.