Axelrod was optioned to Double-A Birmingham after pitching 71/3 innings of three-hit ball that guided the Sox to an 8-1 victory here over the Orioles that halted a two-game losing streak.
After taking the roster spot of the injured Gavin Floyd, Axelrod retired 13 consecutive batters before issuing a walk to J.J. Hardy with one out in the eighth.
He left to a standing ovation from several hundred Sox fans who were equally as pleased with an offense that was 6-for-11 with runners in scoring position.
Alexei Ramirez and Gordon Beckham, the Sox's No. 7 and 9 batters, each had three hits and combined for five RBIs.
The victory, coupled with the Tigers' 1-0 loss to the Royals, extended the Sox's lead over Detroit to three games in the American League Central.
"There's no time to lose games, but Baltimore is in the same spot," Beckham said. "(The Orioles) are playing for a playoff spot."
Ramirez capped a four-run first with a two-run single after Alex Rios had doubled in two runs, and Axelrod's picked everyone up with some help from bench coach Mark Parent.
"After the third inning I came in, and Parent said, 'Trust your stuff,'" Axelrod said. "'You're good enough. Don't nibble.'
"It's simple. But sometimes it just takes that reinforcement. I was able to go out and challenge them for the most part."
Axelrod knew his minor league demotion was more of a technicality because Birmingham's season ends Sunday, and the Sox will recall him immediately so he can start Monday night against the Twins at U.S. Cellular Field.
"It's great because the alternative was (Triple-A) Charlotte," said Axelrod, referring to the fact he would required to stay with the Knights for at least 10 days if he was sent there. "I'm thankful they want me back soon."
Meanwhile , infielder Jose Lopez is expected to be recalled from Charlotte, which will participate in the International League playoffs.
The Sox also could promote a catcher if Tyler Flowers has to leave the team to attend to his wife Nancy, who is expecting the couple's first child.
Those concerns seemed somewhat minor after the offense broke out early and added runs after scoring only three in the previous two games.
"That's stuff the offense can build off," said manager Robin Ventura, who last week stressed the need to manufacture runs without relying on home runs.
Ramirez singled and scored on Beckham's double off the left field wall in the fourth, and Beckham's two-run single in the sixth off reliever Kevin Gregg was set up by Flowers' sacrifice bunt.
"We play our best when those guys are knocking in runs," Ventura said.