Roman Bednar twice put Albion in front, but Ched Evans and then David Cotterill’s controversial late penalty rescued a point for the Blades.
Albion manager Roberto Di Matteo refused to be drawn on the penalty incident.
He said: “I can’t comment too much, otherwise I’ll get banned, but it’s a very hostile place and the supporters make it difficult for referees.
“I thought we did well because Sheffield United are a good team, especially at home, who make your life very difficult.
“We showed resilience and twice went ahead. It was a bit disappointing to concede two goals, especially the first equaliser so soon after we scored, but we can’t be too disappointed because we’re still unbeaten.”
Di Matteo radded that there are unlikely to be any further additions to his squad before the transfer window closes.
“I don’t think we’re going to make any more signings,” he commented.
Early on, United striker Henderson put a header on target which was comfortably gathered by Carson.
During a good spell for Albion, Jerome Thomas had a deflected shot saved by Mark Bunn and Robert Koren put a free-kick wide.
Evans went desperately close to putting the Blades ahead shortly before the break, firing in a 20-yard shot which flashed a fraction wide.
Bednar gave the Baggies the lead early in the second half, heading home at the near post from a Shaun Cummings cross.
The Blades levelled almost immediately, Evans getting his head to a Ward cross.
Bednar scored again shortly afterwards, bringing the ball from Carson’s punt upfield before slotting past the exposed Bunn.
But United equalised just a few minutes from time, Cotterill firing home from the penalty spot after Shelton Martis was ruled to have tripped Henderson.
Sheffield United assistant manager Sam Ellis insisted there was no doubt about the award of the penalty.
He said: “There is no controversy as far as we are concerned. I don’t know if it was one player or two who tripped Darius Henderson up.”
Scorers: Bednar (54) 0-1, Evans (56) 1-1, Bednar (60) 1-2, Cotterill (pen, 88) 2-2.
SHEFFIELD UNITED: Bunn, Walker, Morgan, Kilgallon, Taylor, Ward (Howar,d 90), Montgomery, Quinn, Treacy (Cotterill, 70), Henderson, Evans (Reid, 79). Substitutes: Bennett, France, Bromby, Sharp.
WEST BROMWICH ALBION: Carson, Cummings, Martis, Olsson, Mattock, Thomas (Reid, 73), Koren, Mulumbu, Cech, Bednar, Moore (Dorrans, 58). Substitutes: Kiely, Barnett, Meite, Valero, Cox.
Referee: Phil Crossley (Kent).
Bookings: Sheffield – Henderson; Albion – Mulumbu, Koren, Thomas, Mattock, Bednar.
nTony Mowbray denied Aiden McGeady was a cheat after the Celtic star was shown a second yellow card for diving in the 1-0 Clydesdale Bank Premier League win over Hibernian at Easter Road.
Republic of Ireland international McGeady, booked in the first half for a foul on Derek Riordan, picked up a second caution from referee Dougie McDonald for taking a dive in a touchline challenge with Hibs defender Paul Hanlon.
Mowbray said: “I think the referee has been influenced by the diving situation.
“It was unfortunate for Aiden. It was a poor decision and we are in all in disbelief. You have to put it into the context of the boy travelling 50 yards before the incident. He went to ground because he was knackered.
“Is it a dive? Never in a million years. A dive is when you try to influence the referee, you throw your arms up and so on.”