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Albion have now registered just one league win from six games in front of their own fans, while the Blades have gone three away encounters without a victory.
Midfielder Darren Currie, whose uncle is Blades great Tony, fired Brighton into a 22nd-minute lead when he thumped the ball home from 18 yards after being set up by Leon Knight.
United hit back in the 62nd minute in controversial circumstances through Paul Shaw before Michael Tonge hit the woodwork.
The Blades, who have lost their last two games on their travels, had the better of the opening exchanges - and it required a fine block by Kerry Mayo to deny Shaw a goalscoring chance in the seventh minute.
Adam Virgo, having scored three goals in his last six games since employed as an emergency striker, then tried his luck from 30 yards - but his shot failed to trouble Paddy Kenny in the United goal.
The Blades created the first clear-cut opportunity of the game in the 16th minute when Alan Quinn saw his 18-yard drive well saved by Albion goalkeeper Michel Kuipers.
Knight netted 27 goals, including the play-off winner, to fire the Seagulls into the Championship - but he has struggled to find his form this term.
The diminutive striker, whose sole success has come from the penalty spot, had a chance in the 18th minute to put his side ahead but screwed his shot wide from the edge of the box.
However, the home side went ahead shortly afterwards through Currie's cracker.
Tonge was denied by Kuipers 10 minutes before half-time as the Blades attempted to get back on level terms before debutant Danny Cadamarteri, signed from Leeds on Thursday, was also foiled by the Dutch goalkeeper.
The visitors came out flying in the second half, and Shaw was thwarted by Kuipers within a minute.
Blades boss Neil Warnock threw on Andy Liddell for Tommy Black on the hour - and the move reaped instant reward.
Shaw equalised in controversial circumstances in the 62nd minute when, amid claims of offside, he tucked the ball past Kuipers - who was booked for his protests - from Liddell's centre.
Buoyed by the goal, United came to life and so nearly went ahead six minutes later only to see Tonge's 20-yard drive hit the woodwork.
Kuipers was beginning to work overtime as he kept his side on level terms with 18 minutes remaining, diving to smartly keep out Shaw's effort and then thwarting Cadamarteri from similar range as the Blades pressed for a winner.
Substitute Albert Jarrett had the final chance of the match, but the save was comfortable for Kenny.