"You can't cost your team games trying to learn a job," Schilling said. "You can't do that. There's no excuse for what happened."
Schilling (4-5) entered the game with a two-run lead with two outs in the eighth and struck out Curtis Granderson to end the inning. In the ninth, Schilling gave up three runs on four hits and a walk.
The six-time All-Star was moved from ace to closer a month ago when he returned from an ankle injury. He was out for 2½ months with a bone bruise on his right ankle, the same damaged ankle he pitched on in the AL championship series against New York and the World Series against St. Louis.
Schilling had converted nine saves in 10 opportunities, but had given up four runs on four hits -- including three homers -- in his last two appearances.
"He's not the Curt Schilling that finished last season," teammate Johnny Damon said. "He needs some work, he knows it. He'll find it. Hopefully, he'll get another opportunity (Tuesday) and he'll close it out for us."
Placido Polanco started the rally with a leadoff single in the ninth, Dmitri Young followed with a one-out RBI triple and Magglio Ordonez tied the game with a single. After a walk and a strikeout, McDonald singled to left and as the Tigers celebrated at home plate, Schilling walked toward the dugout visibly dejected.
McDonald was beaming while talking about the most important hit of his career. The utility infielder, acquired last month from Toronto, has bounced between the majors and the minors since his major-league debut with Cleveland in 1999.
"It's been a lot of years of playing baseball to finally feel that," he said. "I've watched a lot of guys get that feeling. I'll remember that for a long time."
McDonald entered the game in the ninth only because Omar Infante made a baserunning mistake, not running hard on a grounder that went from foul to fair territory down the third-base line, leading to the second out of the eighth inning.
"Those are lessons that we need to learn," Tigers manager Alan Trammell said. "I made my statement. I talked to him. It's over."
Jamie Walker (4-3) pitched the ninth for the Tigers, who have won three straight and snapped Boston's six-game winning streak.
The AL-East leading Red Sox appeared to be on their way to another victory behind David Ortiz's 29th home run and Alex Cora's three RBI, two on a homer, before Schilling struggled.
Red Sox starter Bronson Arroyo gave up three runs on 10 hits and no walks over six innings.
"He battled and kept us in that game," catcher Jason Varitek said. "We just couldn't break it open."
Tigers starter Sean Douglass allowed five runs on five hits and four walks over four-plus innings.
Cora's two-run homer put Boston ahead 3-0 in the second after Manny Ramirez doubled and scored on Bill Mueller's sacrifice fly. Infante pulled Detroit within a run with a two-run double in the home half, and Ordonez's sacrifice fly in the third tied it.
Cora's groundout in the fourth scored Ramirez. Ortiz's RBI double gave the Red Sox a 5-3 lead in the fifth, and his homer in the seventh made it 6-3.
- With his divorce two weeks away, Rodriguez said he didn't travel with the team last week to Toronto while he was suspended because he needed to clear his head. The All-Star catcher said he apologized to his teammates for joining them a day later than expected in Kansas City, but he's not sure he has been forgiven. "They don't know what I've been going through all year and they don't need to know because it's my personal business," he said before taking himself out of the lineup Monday. "If they can't accept my apology, that's fine."
- Damon, who is leading the AL in batting, was in the lineup for the first time since leaving Friday night's game in the ninth with a left hamstring injury.
- Detroit SS Carlos Guillen (knee) will be examined Tuesday.
- Two male fans ran across the field naked in the sixth, delaying the game for a couple of minutes.
- The Red Sox will start Jon Papelbon on Tuesday after making a move to promote him from Triple-A Pawtucket and sending down RHP Manny Delcarmen.