Tillman allowed one hit over seven innings, Nick Markakis drove in three runs and Baltimore cruised to a 6-0 victory Tuesday night to extend its winning streak to four.
Lew Ford homered for the second time in two nights and Adam Jones hit his 100th career home run for the Orioles, who moved a season-high 14 games over .500 (71-57) and remained atop the AL wild-card standings.
"If J.J. isn't making the play, then no one's making the play," said Tillman, who lamented his four walks more than that one scratch hit.
"There were plenty of games where I had better stuff," the right-hander insisted. "There were some spurts there when I kind of got out of whack."
Brian Matusz worked the final two innings, allowing one hit in completing Baltimore's seventh shutout.
Sale (15-5) gave up four runs and six hits in four innings, his shortest start of the season. Coming off a 13-strikeout win over the Yankees, the left-hander lost for the second time in six starts since July 21.
Asked why he was removed after only 75 pitches, Sale replied, "Just came to me after the fourth and said that's it for the night. You don't want to get that call. I didn't do anything to help our team win tonight. I kind of put them in a tough spot, pulling the starter after four. I got no one to blame but myself. That's as bad as it gets."
Chicago manager Robin Ventura said, "It was just one of those evenings it didn't look like he had it."
It was the fifth straight road loss for the White Sox, who won six in a row at home before dropping the first two of this four-game series. It was Chicago's most lopsided shutout defeat of the season.
The Orioles have won 12 of 15 at home as they continue toward their first winning season in 15 years, but their scintillating play has not attracted large crowds at Camden Yards this week. Only 12,814 showed up for this one, slightly more than the 10,955 on Monday night.
Those in attendance saw an impressive pitching performance by Tillman, who has as many wins this year as in his previous three seasons combined.
"Tillman shut down one of the game's best offences," Jones said. "Those guys are hitting . He shut that lineup down."
After Sale struck out the first two batters in the second inning, Baltimore used a single by Nate McLouth and two walks to load the bases for Markakis, who drove in three runs with a double to centre.
"It was almost like I hit a brick wall," Sale said. "The first couple of (batters) I felt like I was dialed in, throwing strikes. Then it just got away."
Ford made it 4-0 in the third with a drive to left, making it seven straight games in which Sale has given up at least one home run. The last time Ford homered on successive nights was in 2005, when he homered in three consecutive games with Minnesota.
Manny Machado delivered a sacrifice fly in the sixth and Jones hit an opposite-field shot to right in the seventh. The drive ended a career-high 110 at-bat homerless drought and gave him 25 for the season, tying a career high.
Earlier this week, the slumping Jones said he was on "a vacation." Asked if was back, he replied, "I booked the flight back home. I'm on standby or something. I don't know. But that's why you've got 25 guys here to pick you up."
NOTES: McLouth had a season-high three hits. ... LHP Joe Saunders will make his Orioles debut on Wednesday night, starting against Chicago RHP Dylan Axelrod, who was recalled by the White Sox from Triple-A Charlotte on Tuesday. Axelrod replaces Gavin Floyd, who was placed on the 15-day DL with an elbow injury. ... The last time Baltimore was 14 games over .500 was June 21, 2005 (42-28). ... Chicago C A.J. Pierzynski went 0 for 3 and is hitless in his last 14 at-bats.