The right-hander will try a fourth time to improve to 7-0 on the road Tuesday night against the Chicago White Sox.
Tillman (9-5, 3.68 ERA) is 6-0 with a 4.68 ERA in 13 road starts, but has a 1.69 ERA in his last four since yielding five runs in one-plus inning during an 8-6 loss at Texas on June 5.
He's not pitched away from home since July 23 when he gave up a run in six innings of a 3-2 loss to the Los Angeles Angels.
In Tillman's next start, he gave up five runs - three earned - in five innings of a 7-6, 12-inning victory over the Angels, but has gone 2-0 with a 1.74 ERA in the next three. He's allowed a two-run homer in each of the last two for his only runs over those three, most recently Wednesday in seven innings while not factoring in the decision of a 5-3 win over the New York Yankees.
Tillman is 2-1 with a 4.30 ERA against the White Sox (59-66), but hasn't faced them since 2012.
Markakis, who hit one of his team's three home runs, also robbed Conor Gillaspie of a potential go-ahead homer with a leaping grab in the seventh to help the AL East-leading Orioles (71-52) win their second straight.
''They're pretty much the whole package,'' losing pitcher Chris Sale said. ''You've got to be sharp and on your A-game when they come into town."
Markakis is batting .415 during a 10-game hitting streak, and is 9 for 15 with three RBIs in his last four at Chicago.
He's 1 for his last 7 with three strikeouts against Jose Quintana (6-9, 3.14).
The left-hander gave up five runs in 3 2-3 innings of a 5-3 loss in his first start versus Baltimore in 2012, but has yielded four and fanned 23 over 21 innings to go 1-1 in three since. All four runs have come on solo homers, most recently one from Pearce in seven innings of a 4-2 victory June 24.
''He's a guy that short arms the ball and the ball jumps out of his hand," Markakis said. "It is tough to get in a rhythm when you don't see the ball behind his back."
Quintana went 3-0 with a 1.69 ERA during a nine-start stretch prior to posting a 4.38 ERA while losing his last two. He left in the seventh of a 7-1 loss at San Francisco on Wednesday, when he was charged with four of the seven runs scored in an inning that featured an overturned blocking-the-plate call.
Nelson Cruz is 2 for his last 6 with a home run against Quintana. He hit his 32nd on Monday to surpass Chicago's Jose Abreu for the AL lead.
Abreu has gone 18 straight contests without homering.
Chicago's Avisail Garcia had a two-run single, and is 4 for 10 with three RBIs in three games since missing four months with a shoulder injury.
Alexei Ramirez is 4 for 6 with a homer against Tillman.