Carlisle striker Joe Garner had an eventful game as he cancelled out Luke Beckett's opener for Huddersfield before being sent off.
Huddersfield took the lead in blustery conditions when Andy Taylor's cross was met by Beckett's glancing header.
Carlisle equalised in added time at the end of the first-half when Garner bundled in Jeff Smith's free-kick.
But Garner was sent off in the 90th minute when he was booked twice in quick succession.
Carlisle: Westwood, Raven, Livesey, Murphy, Aranalde, Johann Smith (Gall 46), Joyce (Lumsdon 79), Thirlwell, Jeff Smith, Garner, Graham (Holmes 79).
Subs Not Used: Williams, Gray.
Sent Off: Garner (90).
Booked: Thirlwell, Garner.
Goals: Garner 45.
Huddersfield: Glennon, Holdsworth, Mirfin, Sinclair, Taylor, Taylor-Fletcher, Worthington, Collins, Schofield, Beckett, Hayes (Booth 69).
Subs Not Used: Eastwood, Hudson, McIntosh, Young.
Booked: Taylor, Taylor-Fletcher.
Goals: Beckett 26.
Ref: S Mathieson (Cheshire).