The Cleveland bullpen also played a role, too.
Salazar struck out nine in 3 2-3 innings, Raburn hit an RBI double in the fifth, and the Indians earned a 3-1 win Friday over the Chicago White Sox.
Cleveland defeated Chicago for the 10th consecutive time this season and leads the season series 13-2. The Indians have outscored Chicago 91-49 with four games left between the teams.
Salazar is the first Indians starting pitcher since 1916 to strike out at least nine batters in less than four innings.
"Today I felt good," Salazar said. "Too many pitches."
The bullpen, however, made up for that.
Hagadone, the first of seven relievers, got pinch-hitter Josh Phegley to ground out and end the fourth. It culminated with Chris Perez earning his 24th save in 28 chances, getting Paul Konerko to fly to centre with runners on first and second to end the game.
Combined, the seven Cleveland relievers pitched 5 1-3 innings and only one unearned run. Bryan Shaw (4-3) threw two innings for the win.
"It's been good to be able to match up like we have," said Matt Albers, who threw a scoreless third of an inning. "We've got quite a few left-handed power arms and we've got some righties who can get some guys up. We can probably just match up from the seventh inning on."
Raburn went 1 for 3 before getting removed for a pinch-runner in the fifth, one day after playing for the third time since Aug. 18 because of a left heel injury.
Raburn has 17 homers and 67 RBIs against the White Sox in 90 games, and his double in the fifth gave the Indians a 2-0 lead.
It wasn't quite like Thursday when he went 3 for 3 with a homer and five RBIs, but it was enough for Cleveland.
"Just trying to have good at-bats," Raburn said. "That's all I'm doing."
The White Sox aren't really doing that, and it prevented them from overcoming a short outing by their starter.
Hector Santiago (4-9) remained winless since Aug. 18 for Chicago, going four innings and giving up three runs and six hits while walking three.
Santiago's outing was his second shortest since pitching 2 1-3 against the Indians on June 28, when he gave up five earned runs.
Unlike White Sox manager Robin Ventura, who said Santiago's wildness might have been caused by fatigue, Santiago was adamant that wasn't the case.
"I don't think it had anything to do with tiredness," said Santiago, who's thrown 142 2-3 innings. "The velocity's still there. They battled. I feel like I made good pitches."
Santiago and the Chicago pitchers also got little support from the struggling White Sox lineup.
Chicago was held to three runs or fewer for the 74th time and has scored five runs in its past four games, all losses. The White Sox have dropped 13 of 15 and fell a season-high 31 games below .500.
Chicago's best threat came in the seventh trailing 3-1 when Danks and Marcus Semien singled to start the inning against Cody Allen.
Alexei Ramirez then lined out to short, and Allen was replaced by Marc Rzepczynski, who struck out Dunn for the second out of the inning. Albers relieved Rzepczynski and got Konerko to ground to third.
Chicago left 13 on base and was 2 for 12 with runners in scoring position.
"We did (have opportunities). Even in the last inning, guys still get on base to try and get something going. We had a couple of balls hit hard," Ventura said. "Paulie hit his well and Jordan the same thing. We just couldn't cash that one hit in when we needed it."
The Indians did.
"Today we didn't have a ton of runs, but we made their starter throw a lot of pitches and we got him out of the game and sometimes that's the way you win," Indians manager Terry Francona said.
NOTES: Cleveland RHP Justin Masterson played catch from 75 feet on Friday, one day after throwing from 60. Masterson hasn't pitched since Sept. 2 when he left his start against Baltimore with a strained left oblique. ... Cleveland is carrying 15 relief pitchers, and Francona was asked if it's hard to restrain himself from immediately going to the bullpen when a starter first falters. "I think, when you don't give your starter a chance, as long as their stuff looks OK, I think you're asking for trouble," Francona said. ... Dunn went 0 for 4 and dropped to 3 for 34 over his past 10 games. . Saturday's pitching matchup is Cleveland's Ubaldo Jimenez (11-9, 3.62) against Chicago's Andre Rienzo (2-1, 4.50).