Rotherham United lost ground on the League One pace-setters after failing to beat 10-man opposition.
Conor Townsend was sent off in first-half stoppage time but Rotherham could not take advantage.
Millers’ Michael O’Connor was thwarted by visiting goalkeeper Ben Amos, before Carlisle’s Sean O’Hanlon had a header tipped over by Adam Collin.
Townsend was then booked twice in three minutes to take an early bath.
A second-half rearguard saw Carlisle keep Rotherham out with Tom Eaves seeing his 78th-minute strike blocked by Amos.
The draw leaves Steve Evans’s side 10th in League One.