The Terriers twice saw shots cleared off the line and also saw striker Alan Lee hit the crossbar. Substitute Lee rattled the woodwork in the second minute of stoppage time from a Kevin Kilbane cross while seconds later Peter Clarke had an effort hacked off the line in a goalmouth scramble and right at the death Swindon's David Prutton earned a point for the visitors by clearing Jamie McCombe's header.
Striker Jordan Rhodes also hit the bar with a header in the first half as Huddersfield equalled an 86-year-old club record.
A draw extends Town's unbeaten run to 17 League games, matching a record set in 1925.
Swindon though nearly won it themselves when Matt Ritchie hit the post from Calvin Andrew's pull back.