The incident boosted the hosts, who went on to dominate possession throughout the remainder of the first half but could not find a way past Lukasz Fabianski in the Swans goal.
The second half brought about more of the same as the Terriers continued to send forth waves of attacks against Carlos Carvalhal's charges.
Nonetheless, Fabianski was forced into just one save of note, tipping Mounie's fierce volley onto the bar midway through the second period.
Huddersfield enjoyed more than 80% of possession and came within a whisker of victory as Tom Ince hit the post in injury time with a downward header.
However, Swansea held firm right until the very end and were able to claim an unlikely share of the spoils come the final whistle.
HUDDERSFIELD TOWN (4-2-3-1): Lossl; Hadergjonaj, Malone, Jorgensen, Schindler; Hogg, Mooy (Williams 69'); Van La Parra (Depoitre 77'), Pritchard (Quaner 64'), Ince; Mounie
SWANSEA CITY (3-5-2): Fabianski; Van der Hoorn, Fernandez, Mawson; Naughton, King, Ki, Clucas, Olsson; J. Ayew, A. Ayew (Abraham 72')