The rookie right-hander allowed just three hits over 6 2/3 innings, struck out eight and managed to keep the White Sox off the board. But Chicago starter Carlos Rodon was equally impressive in throwing eight shutout innings, which made Bieber's performance even more critical despite Palka's ninth-inning heroics.
"It's been nice -- just another outing to try to build off of," said Bieber, who threw 74 of his 106 pitches for strikes. "There is a lot of room for improvement as always, but (I'm) just trying to get my feet under me and try to build momentum."
Added manager Terry Francona: "I thought he was tremendous."
The Indians threatened in the ninth, hoping to notch another last-minute win. But after putting runners on first and second with just one out, Cleveland couldn't manage a run. White Sox reliever Jace Fry struck out Yan Gomes on the 11th pitch of his at-bat and then got Jason Kipnis to pop out to end the inning.
Palka, who struck out in his first three at-bats, ended the game minutes later, launching the game-winner into the left-field bleachers with two strikes on a 96-mph Ramirez fastball.
All five Indians who reached scoring position were prevented from scoring as Rodon minimized the damage throughout his outing, during which he allowed just four hits.
Leadoff hitter Francisco Lindor also saw his five-game string of multi-hit games end after he finished 1-for-3 with a walk. Lindor doubled in the second inning, but grounded out twice as the streak ended one game shy of a career high.
Like he did with Lindor, Rodon had a lot to do with shutting the Indians down.
"We've seen him pitch good before, but he was on top of his game tonight," Francona said.
Indians designated hitter Edwin Encarnacion left the game before his at-bat in the fourth inning with left arm soreness. Encarnacion has been dealing with a right hand bruise, which he said after Friday's game has made swinging a bat with two hands painful. Francona said because Encarnacion has been overcompensating due to the hand injury, he was experiencing pain in his left biceps.
MOMENT THAT MATTERED Bieber preserved the scoreless tie in the fifth inning despite allowing a leadoff double to Yoan Moncada. Bieber struck out Ryan LaMarre and then got pinch-hitter Adam Engel to foul off a bunt attempt for a third strike before avoiding damage when Yolmer Sanchez flied out to right to end the threat. He credited his catcher, Gomes, for navigating him out of trouble.
"I was able to trust him, and how he knows these hitters," Bieber said. "He obviously knows these hitters a lot better than I do."
HE SAID IT "I've always felt I have a tendency to get stronger. Later in games, the more comfortable I get. I haven't necessarily shown that a lot since I've been up here, so it was nice to be able to extend it a little bit. I went out there and competed." -- Bieber
UP NEXT Trevor Bauer will be looking for another strong outing Saturday after the right-hander didn't allow an earned run, struck out 11 and allowed just three hits in his last start against the Twins. He reached double-digit strikeouts for the ninth time this season during the outing. Bauer (11-6, 2.25 ERA) will face James Shields (4-13, 4.50) in the second game of the three-game set against the White Sox at Guaranteed Rate Field, which is set for a 7:10 p.m. ET start.
Jeff Arnold is a contributor to MLB.com based in Chicago.