
Boston swept the Angels in the first round in 2004 and last year, both times en route to World Series titles.
"What happened in '04 or 1986 does not matter to us," Red Sox manager Terry Francona said. "We set out to win today's game. It was difficult, but we did it. Now we'll go prepare for the next game."
Game 3 will be Sunday night in Boston, with Joe Saunders pitching for the Angels against Josh Beckett, who was pushed back from the opener after injuring a muscle in his side.
"There is a challenge in front of us and the only way to meet it is going to be pitch by pitch, inning by inning on Sunday," Angels manager Mike Scioscia said. "We played well in their park all year, and we have to do it now."
Drew's RBI double and Jason Bay's three-run homer off Ervin Santana gave Boston a 4-0 lead in the first inning, but the Angels, 100-62 during the regular season, clawed back. Los Angeles tied the score in the eighth when Chone Figgins hit a leadoff triple off Justin Masterson - the Angels' first extra-base hit of the series after 19 singles - and Mark Teixeira hit a one-out sacrifice fly against Jonathan Papelbon (1-0).
Rodriguez (0-1), who set a record with 62 saves in the regular season, allowed a leadoff double to David Ortiz in the ninth on a ball that bounced out of the glove of Reggie Willits, who tried for a leaping catch at the wall in right-center. After Kevin Youkilis grounded out, Drew pounced on a 2-2 changeup and sent it deep over the wall in center.
"It just worked out that I squared it up really nice," Drew said.
Rodriguez, who allowed a game-ending home run to Manny Ramirez in Game 2 last year, hung his head, then covered much of his face with his glove.
"He's one of the best pitchers in the league," Ortiz said. "If you get a pitch you like, you better hit it. You might not see it again."
Papelbon retired all six batters he faced, getting help from Youkilis in the ninth. The third baseman caught pinch-hitter Gary Matthews Jr.'s foul popup with a terrific leaping grab over a camera well for the second out. Papelbon then struck out Howie Kendrick to end the game, and the closer pumped his arms and pounded his chest after his final pitch.
"That's kind of the situations I live for," Papelbon said. "We definitely came here and took care of business, but there's business still to be finished."
The Angels, who have lost nine consecutive postseason games, stranded 11 runners - all in the first seven innings. They are 4-for-21 (.190) with runners in scoring position in the two losses, stranding 20 runners overall.