Carlisle midfielder Liam Noble came closest to breaking the deadlock, but his 44th-minute drive came back off a post before the visitors had defender Sean O'Hanlon sent off for a second bookable offence 16 minutes from the end.
In a tight opening 45 minutes, Carlisle winger Jon-Paul McGovern saw his 20-yard drive turned away by Blades goalkeeper George Long, while visiting goalkeeper Mark Gillespie was forced to palm Kevin McDonald's stinging half-volley behind for a corner at the other end.
Blades loanee Jonathan Forte should have put the home side ahead in the 67th minute, but he scuffed wide when well placed after being teed-up by substitute Joe Ironside.
Cumbrians centre-half O'Hanlon then headed narrowly wide of Long's goal, moments before he was dismissed following a foul on teenage forward Ironside.
The Blades pushed hard for a winner in their quest for automatic promotion, but Greg Abbott's hard-working side held on for a point.