Steven Gillespie handed the U's a third-minute lead with his 10th goal in 11 games, and that was the way in remained until Anthony Wordsworth saw his late penalty parried by Alex Smithies and then Magnus Okuonghae headed into his own net in the fifth minute of stoppage time.
Gillespie's opener came after he closed down Smithies' attempted clearance just outside the area and the ball looped into the air and into the vacant goal.
The Terriers came close to equalising just after the hour mark when Danny Ward's first-time effort from close range clattered the crossbar.
Smithies parried away Andy Bond's fierce shot soon after and denied Kayode Odejayi, before saving Wordsworth's 88th-minute spot-kick after Peter Clarke had fouled Kem Izzet in the area.
And there was more late misery for the hosts as Huddersfield claimed a dramatic point when Okuonghae headed over 'keeper Ben Williams and into his own empty net.