The home side took the lead through Shane Long but it was Defender Ulises De la Cruz strike which put the game into discontent.
After coming on the field as a second half substitute Keith Gillespie was, in the 55th minute sent off after being on the pitch just 10 seconds. And, after a tussle in the dugouts Neil Warnock and Reading's Wally Downes were also given their marching orders.
Reading forced a third goal through Stephen Hunt before Christian nade beat an offside trap to give United some hope.
The result leaves the Blades just four points from safety whilst Reading realistically require a further two victories cement their place in next seasons Premiership race.
The Royals could have took an early lead but Ivar Ingimarsson headed over the top at a Glen Little corner after he shrugged off his marker.
Little hinted he could be the prime outlet for Reading by tricking his way past Derek Geary to deliver threatening crosses which screamed out for the sort of finishing touch the injured Kevin Doyle might have provided.
The Blades' ploy to over-populate midfield made for a scrappy encounter but had the desired effect as Reading laboured to create anything going forward.
It was 38 minutes until either keeper was worked, with Paddy Kenny plunging to tip away Graeme Murty's long-range effort.
Leroy Lita missed a great opportunity when he beat Kenny to a through ball and with Davis covering on the goal-line, fired the ball into the side-netting.
Reading went ahead just before the break when Steve Sidwell surged into the box and got a break when Chris Lucketti's clearance rebounded off him and into the path of Long who tucked the chance away from close-range.
The Blades' hopes of getting back into the game were hit when Reading doubled their lead through De la Cruz.
There was another large slice of fortune involved as the Ecuador defender's surge from the left-back berth was initially halted by Stephen Quinn's challenge, but the ball again fell kindly for James Harper.
Hunt's pass found the Ecuadorian continuing his forward run and the left-back finished coolly from the inside-right position.
But Reading's second goal was merely the spark to ignite an explosion in the match.
Within 10 seconds of coming on as substitute Gillespie was heading back down the tunnel after being shown a red card by referee Mark Halsey for throwing an elbow in the direction of Hunt.
As Gillespie headed down the tunnel he threw another punch at Hunt, and as tempers rose, backroom staff from both sides became involved.
Reading coach Downes was sent from the touchline for shoving Blades' boss Warnock, who followed him to the stands.
A football match eventually broke out again, but Sheffield's hopes of getting back into the game not only disappeared down the tunnel with Gillespie, but with a third Reading goal.
Reading took advantage of their man advantage by working the ball wide and although Rob Kozluk blocked Sidwell's initial shot, the ball fell kindly for Hunt who reacted sharply to turn the loose ball home.
Sheffield United at least had the consolation of a goal, when slack defending at a free-kick left Nade clear to score from eight yards.