Beckett, the 2003 World Series Most Valuable Player, surrendered an infield single to Reid Brignac in the third inning, then breezed through 19 consecutive batters to end the game.
Beckett struck out six batters, had no walks and needed only 97 pitches to record his first shutout since July 2009.
After posting a 6-6 win-loss record during an injury-plagued season in 2010, Beckett is now 6-2 and leads the American League with a 1.86 ERA.
(Writing by Jahmal Corner in Los Angeles. Edited by Patrick Johnston)