ANAHEIM, Calif.—J.D. Drew looked pretty feeble as he swung and missed a pair of off-speed pitches from Francisco Rodriguez. He sure didn’t miss a third one.

Drew hit a towering two-run homer off Rodriguez in the ninth inning, giving the Boston Red Sox a 7-5 victory over the Los Angeles Angels on Friday night and a 2-0 lead in their first-round AL playoff series.

So now, thanks to another Boston postseason victory over the Angels, the team with baseball’s best record this year is on the verge of elimination.

“We’ve always been good about turning the page on a...

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