England striker Peter Crouch celebrates after scoring the second goal.
Winger Joe Cole gave Steve McClaren's side a 37th-minute lead with a crisp half-volley before Beckham set up Crouch for the second in the 54th minute.
Crouch cleverly headed past Estonia keeper Mart Poom on the bounce off a cross from Beckham for his 12th goal in 19 internationals.
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