Bournemouth 0 Huddersfield Town 1
Beckett scored the winner on the opening day against Yeovil and might have scored more as Bournemouth struggled to cope with his experience.
His goal came in the 43rd minute when he was unchallenged as he rose to meet a free -ick from Matthew Young to score with a firm header into the roof of the net.
Five minutes earlier Beckett had again outwitted the Bournemouth defence to head against the inside of a post.
Bournemouth owed a debt to their teenage goalkeeper Asmir Begovic, who blocked a shot from Malvin Kamara in the first half with his legs and then dived to his left to push away a goal-bound shot from Jonathan Worthington.
Apart from a couple of long-range shots from Garreth O'Connor and Darren Anderton, Bournemouth had nothing to show for some attractive approach work.
It was not until the last few minutes, with defeat staring them in the face, that they began to trouble Huddersfield and put them under concerted pressure.
In the 88th minute substitute Max Gradel should have equalised but with only the goalkeeper to beat, shot across the face of the goal.
Then in injury time Paul Telfer cut in from the right and his right-foot shot was destined for the top corner until Matt Glennon got across to push the shot to safety.
Bournemouth's only other chance fell to another substitute, 17-year-old Sam Vokes, who turned sharply on the edge of the area but lofted his shot over the bar from a good position.
Huddersfield showed plenty of pace in attack and Beckett and Kamara posed constant threats, leaving Bournemouth without a goal from their first three matches of the season.