The Blades scored midway through the second half when Conor Coady shot home from close range, but the hosts replied through Dean Cox eight minutes from time to earn a point from the contest at the Matchroom Stadium.
The result lifted Nigel Clough's side out of the relegation zone and saw Orient move to 43 points, as many as Wolverhampton Wanderers, but with a superior goal difference.
It ended United's run of five successive League One defeats and kept their place in the playoff spots.
At the other end of the table, Crewe Alexandra are third from bottom despite a narrow 1-0 home victory over Crawley Town.
Chukwuemeka Aneke scored the winner for the hosts at Gresty Road nine minutes from time in a match that saw his side lose Vadaine Oliver to a red card in the 55th minute.
Elsewhere in League One on Saturday, Walsall went down 2-0 to Port Vale at home, Shrewsbury beat fourth-from-bottom Stevenage 3-1 at Lamex Stadium and Coventry City came from behind to register a 3-1 away victory over MK Dons.
Results in full: Crewe 1-0 Crawley, Leyton Orient 1-1 Sheffield United, MK Dons 1-3 Coventry City, Notts County 0-1 Brentford, Peterborough United 1-0 Wolverhampton Wanderers, Preston North End 1-0 Bristol Citty, Rotherham 4-1 Gillingahm, Stevenage 1-3 Shrewsbury, Swindon 3-1 Carlisle, Tranmere 2-1 Colchester, Walsall 0-2 Port Vale