Drew collected four RBIs on the night.
Orioles reliever Matt Albers took the loss and squandered a solid performance from rookie right-hander David Hernandez. Albers gave up two runs and two hits in one-third of an inning during the seventh.
Hernandez left with the game tied 3-3 following the sixth inning. He allowed seven hits, while recording four strikeouts and three walks.
Manager Dave Trembley called it Hernandez's "best outing in a while."
"I thought from the first inning, he threw his breaking ball better," Trembley said. "When he struck out Youkilis, he was more than a one-pitch guy. He's predominantly a fly-ball pitcher. In order for him to be effective, he's got to throw his secondary pitches, and his breaking ball was better and he did have his fastball down more. That was a good, strong outing for him."
Once Albers entered, however, momentum quickly turned in Boston's favor. Alberto Castillo replaced Albers and did not fare any better, giving up three hits and a run.
"Obviously, you're disappointed that you lost and you're disappointed that you lost the fashion that you did," Trembley said. "The game got out of hand after [Hernandez] left the game. We did not get the outs from Albers and Castillo that we expected to get. Both those guys have been pitching rather well for us. It did not happen."
For his part, Albers said he "left a couple of pitches over the plate."
In his brief seventh-inning appearance, Albers gave up a single to Boston second baseman Dustin Pedroia, who then stole second. Pedroia moved to third on a Victor Martinez groundout and was driven in on a single by Youkilis.
"I was trying to get them to chase a pitch that wasn't there," Albers said of his battles with the Red Sox's lineup. "I didn't want to walk Pedroia the first time around and gave in. With Youkilis ... I left it up a little."
Boston's Jon Lester went six-plus innings and gave up 10 hits to improve to 14-7.
Baltimore got things going against Lester in the first, when the southpaw gave up a leadoff double to Brian Roberts. The Orioles' second baseman scored two batters later on a Matt Wieters single to give his team a 1-0 lead.
"It would have been nice to score more than one, but we didn't," Trembley said.
Wieters had three singles on the night.
The Red Sox got a two-run home run from Josh Reddick, who got the nod over an ill Jason Bay, for a 2-1 lead in the second. The Orioles reclaimed the lead thanks to solo home runs from first baseman Ty Wigginton and Melvin Mora in the second and fourth innings, respectively.
The Red Sox tied the game at 3 in the sixth inning when David Ortiz scored on a Mike Lowell single.
Hernandez has given up 24 home runs in his rookie season, but he looked like a veteran against the Red Sox.
"They're all very good hitters," Hernandez said. "You've just got to take one hitter at a time and go from there. Anytime you can go and pitch against Boston, New York, all the playoff contending teams, it's a boost to your morale when you can get through six against a team like that."
With the game's result pretty much decided, the Orioles still put together a minor rally in the ninth inning.
Wigginton hit his second home run of the night, this time coming off Manny Delcarmen. It was the second multihomer game of the season for the first baseman and ninth of his career.
Felix Pie immediately followed Wigginton with a 406-foot shot to center field to cut the score to 11-5. Ramon Ramirez replaced Delcarmen to finish off the game.