Rodriguez, inserted into the No. 2 spot in the batting order with Derek Jeter out of the lineup, lined a 2-2 Tillman pitch into the right-center field seats for a solo homer.
Markakis, a year and a day since a Sabathia pitch broke his left thumb and ended his 2012 season, led off with a ground-rule double.
"There's a risk you take going out between those white lines every day, and it was just unfortunate bad timing last year, but I'm here now in a similar situation and we have to finish up strong," Markakis said.
He was bunted to third by Machado and scored on an Adam Jones' sacrifice fly to center.
NOTES: Rodriguez hit second for the first time since August 2006. ... Jeter missed his second straight game with a sore left ankle. ... The Yankees reinstated OF Zoilo Almonte (sprained left ankle) from the disabled list. ... Orioles 2B Brian Roberts was given the night off until he flied out as an eighth-inning pinch hitter. Casilla (16-for-31 in his career against Sabathia) got the start, and he wound up 1-for-3. ... Yankees RHP Ivan Nova (8-4, 3.02 ERA) pitches Tuesday against RHP Miguel Gonzalez (9-7, 3.98).