Lackey (9-2) was attempting to become the first pitcher to no-hit the Red Sox at Fenway Park since Detroit's Jim Bunning accomplished the feat on July 20, 1958. The 29-year-old allowed two runs on two hits with a pair of walks.
Lackey struck out Jacoby Ellsbury to come within two outs of the Angels first no-hitter since Mark Langston and Mike Witt combined to no-hit Seattle on April 11, 1990. But Dustin Pedroia singled to break up the bid and Kevin Youkilis followed with a two-run homer.
Garret Anderson hit a two-run homer and Maicer Izturis had two RBI for the AL West-leaders, who have won six of their last seven games.
Clay Buchholz (2-6) took the loss after allowing six runs on six hits in 6 1/3 innings.