The former Chesterfield ace, on loan at the Galpharm Stadium from Sheffield United, turned in Jonathan Worthington's cross on 34 minutes and then ran onto Andy Booth's through ball in first half stoppage time to crack in an unstoppable drive.
Beckett looked to have completed a brilliant hat-trick on 86 minutes when he thrashed a terrific 25 yarder into the net from another through ball.
Most people in the ground thought the goal would seal a 4-2 win for the home side but it gradually dawned on them that the linesman was flagging for offside - even though replays showed he was not when the ball was played to him.
Earlier, Pawel Abbott put Huddersfield ahead on eight minutes with a penalty awarded after Booth was pushed over in the box by Shaun Maher.
Just before Beckett got his second Bournemouth striker James Hayter - who had been out of the side for five weeks with a hamstring injury - bag the first of his brace by heading in Wade Elliott's by line cross.
Town lead 3-1 at the break but the home side looked as if they were going to throw it away. Soon after the restart Hayter brought the visitors right back in it by turning in John Spicer's centre and from then on the Cherries dominated.
Elliott and Gareth O'Connor suddenly grabbed hold of midfield and started pushing Huddersfield back into their own half for long periods. An equaliser seemed inevitable but both Hayter and Steve Fletcher missed from close range.
Hayter then missed a glorious chance to complete a fine hat-trick in the closing stages. O'Connor put him through, but as he romped goalwards he showed too much of the ball to Huddersfield keeper Paul Rachubka and gave him the chance to whip the ball off his toes.