Clarke was booked for a foul in the 19th minute and then a clumsy challenge on Jamie Cureton earned him another in the 64th.
The combative Clarke will now miss one of Huddersfield's play-off matches next week to leave manager Peter Jackson with a problem in deciding who to bring in to the team.
Jackson had already replaced his namesake, Nathan Clarke, at half-time fearing a possible red card because he had been booked for a foul.
Huddersfield went into the match already assured of a place in the play-offs and Jackson showed his intentions by leaving out leading scorer Andy Booth and several other key members of his squad in preparation for tough matches ahead.
Already relegated Swindon improved after a poor first half and could have bade farewell to League One with a morale-boosting victory had it not been for Huddersfield goalkeeper Paul Rachubka.
Rachubka made outstanding saves from Chris McPhee, substitute Cureton and then near the end from Lucas Jutkiewicz.
In addition Swindon almost snatched a winner when Ricky Shakes headed against the inside of the post from six yards from a centre by Aaron Brown when it looked easier to score.
Huddersfield offered little as an attacking threat without Booth but almost went home with three points after an incident in the 84th minute.
Lanky substitute John McAliskey seized on an error by Swindon defender Jerel Ifil and almost deceived the retreating Rhys Evans with a cheeky lob from 25 yards which clipped the top of the bar.
Huddersfield also had midfield player Adnan Ahmed booked for a foul while Swindon's Michael Pook was also shown a yellow card.
Swindon lost key defender Sean O'Hanlon in the 41st minute after he had been injured in a clash but the Robins re-arranged their defence to cope with his absence.