Youkilis hit a high fly ball to the deepest part of Fenway Park and center fielder Grady Sizemore chased after it. He couldn't get to it before it hit the side of the Red Sox bullpen and kicked toward left field, where right fielder Trot Nixon ran it down.
Nixon - who happened to hit the last inside-the-park homer for the Red Sox, on July 15, 2005, against the Yankees - made a throw to the cutoff man but Youkilis was already coasting across the plate. From there, he retired to the dugout and, smiling and huffing heavily, assumed the fetal position on the bench.
Youkilis, who also doubled in the fourth, has hit in 20 consecutive games, raising his average from .280 to .354 - fourth in the AL.
Manny Ramirez also homered, moving into a tie for 25th on the career list with No. 478. Dustin Pedroia was 3-for-3 with two doubles and a walk.
Jonathan Papelbon pitched the ninth for his 13th save, but not before putting the first three batters on.
Josh Barfield doubled off the Green Monster to make it 5-3, then Papelbon struck out Casey Blake and Travis Hafner to snap Cleveland's four-game winning streak.
Schilling (5-2) beat Cliff Lee (2-2) in a matchup of pitchers coming off their season worsts.
Schilling gave up five earned runs and 12 hits in six innings against the Yankees on Wednesday. But he allowed the Indians just one run and six hits, fanning 10 or more for the 93rd time in his career, and his first this season.
He tipped his cap to acknowledge a standing ovation when he left after seven innings. The biggest ovation of the game, though, was to welcome Nixon back to Fenway - his first visit in an opposing uniform after 13 seasons in the Red Sox organization.
Nixon and his wife received an award from the Jimmy Fund before the game for their charitable work, and Kathryn Nixon threw out the first pitch. Nixon received another warm welcome when he came to the plate in the second, and Schilling stood off the mound to give the applause a chance to build.
After tipping his cap, Nixon singled to right field, where J.D. Drew replaced him after leaving as a free agent.