Both sides finished Saturday’s League One clash at The Valley with 10 men after substitutes Darel Russell and James Beattie saw red late on and although the Blades began brightly, they were undone when Charlton were awarded a free-kick following a foul on Danny Hollands by Neil Collins 25 yards from Steve Simonsen’s goal.
Addicks skipper Jackson scored in almost identical circumstances in last week’s 1-0 win at Sheffield Wednesday and repeated the feat by smashing his 21st-minute free-kick past Simonsen to put the leaders in front.
United had a goal ruled out after Richard Cresswell was adjudged to have fouled goalkeeper Ben Hamer, while Harry Maguire headed just over the crossbar before the break.
Hamer almost gifted the Blades a 67th-minute equaliser when the Addicks keeper dropped the ball, but Ched Evans failed to capitalise and placed his shot over the bar.
Both teams were reduced to 10 men in the 85th minute when Addicks substitute Russell went in for a challenge on Kevin McDonald with his studs showing and Beattie received his marching orders for violent conduct after an offence spotted by the linesman in the melee that followed.