Beckett, who joined Town last month from Sheffield United, latched onto a loose ball and chipped Hatters keeper Marlon Beresford from 20 yards.
Suffolk based referee Mick Thorpe added six minutes and 45 seconds of stoppage time at the end off the game to make up for Luton's second half time wasting with Town punishing Luton for their spoiling tactics.
The visitors spent most of the second half kicking the ball away at set pieces and feigning injury at every opportunity in a bid to cling on to their controversial lead.
Croatian midfielder Ahmet Brkovic gave Luton the lead on 33 minutes with a close range tap in - though most home fans believed that he and Steven Howard were both offside as they tried to reach Kevin Foley's cross from the right.
Referee Thorpe waved play on and when Howard scuffed at an attempt to shoot Brkovic nipped in ahead of David Mirfin to score.
Video replays proved inconclusive though Huddersfield supporters had made up their minds and jeered the officials at half time.
Town dominated the match until Luton scored with both Foley and Russell Perrett having to make superb last-ditch tackles on Beckett and Andy Booth to prevent them scoring on 26 and 32 minutes respectively.
After the break Town again dominated with Rob Edwards' hitting the side netting from 25 yards with a powerful drive and then Town stepped up for an equaliser. Manager Peter Jackson switched formation from 4-4-2 to 4-3-3.
Jackson also made some late substitutions that left Huddersfield with four strikers on the field during a frantic closing spell. Shortly before Beckett equalised, he forced Marlon Beresford into a fine save with a curling shot struck from about 15 yards after he expertly controlled Danny Schofield's pass.