Keith Gillespie's spectacular late strike gave Sheffield United all three points and left Charlton rooted to the bottom of the Premiership.
Jagielka (right) tried to marshall Reid
Andy Reid gave Charlton the lead, tapping in Paddy Kenny's parry from Darren Ambrose's shot.
Skipper Chris Morgan equalised midway through the second half when he headed in Gillespie's left-wing corner.
It looked odds-on for a draw until Gillespie met a Charlton clearance with a fierce volley from outside the area.
The win lifts the Neil Warnock's men out of the relegation zone, while the defeat for Charlton leaves them in a desperate situation.
The game was a highly entertaining affair. Two players, in particular, were responsible for much of the excitement - United's Hulse and Charlton's Reid.
Midfielder Reid carried his side with his tireless running and invention, while striker Hulse was a thorn in the side of the Addicks defence.
However, as good as Hulse's timing and positioning was in and around the area, poor finishing let him down.
He twice headed wide from short range in the first half and when he did find the target, with a swivel and shot, Charlton keeper Carson was alert to the danger.
Charlton created few chances, but when they did venture into their own half, often the attacks were led by Reid.
The former Spurs player started and finished the move which led to their goal, which came against the run of play.
United lost the ball in midfield to Reid who ran up to the penalty area and played in Ambrose.
The former Newcastle midfielder's low shot was parried by Carson, but only to the feet of Reid, who finished from close range.
The Blades came out with guns blazing after the break.
But after Derek Geary's inexplicable headed miss within minutes of the restart, Warnock and his boys must have thought the gods were not not smiling on them.
However, cometh the hour (64 minutes to be precise), cometh the man. That man was captain Morgan, who bulleted home Gillespie's in-swinging corner to give his side a deserved equaliser.
Morgan, like Hulse, also came close to scoring earlier on with two headers, but the impressive Carson was on hand to block both.
The Blades went looking for the winner right until the death and they got their reward courtesy of Gillespie's sublime effort.
It was heartbreaking for Charlton, but the ecstatic home fans would not have cared in the slightest.
Sheffield United manager Neil Warnock:
"It's seven years today since I first came to Sheffield United, it was my 58th birthday yesterday - it's just a great weekend for me.
"There were times when people must have wondered if we were ever going to score because we created so many chances, more than we have ever done.
"By being sloppy and giving them a goal, it gave them something to hang on to, and with our bad finishing it was always going to be difficult to come back.
"But I told the lads at half-time not to get frustrated, that they could score twice in a minute - the 93rd and 94th minutes if necessary.
"Thankfully they came a little bit earlier than that."
Charlton head coach Les Reed:
"After getting our noses in front, I am very disappointed we've not taken something from this game.
"We have to learn how to win, and how to hang onto a lead once we have taken it.
"I was satisfied to go in at the break 1-0 up, particularly as we had not played well, but we at least had something to fight for in a bid to come away with a point.
"We should have held on and got something from the game, but having said that, Sheffield United deserved the victory because they created a lot of chances."
Sheff Utd: Kenny, Geary, Bromby, Morgan, Kozluk, Gillespie, Montgomery, Jagielka, Stephen Quinn (Kazim-Richards 76), Hulse, Nade (Webber 71).
Subs Not Used: Sommeil, Lucketti, Law.
Goals: Morgan 64, Gillespie 88.
Charlton: Carson, Young, El Karkouri, Hreidarsson, Traore, Rommedahl (Marcus Bent 67), Holland, Faye (Sam 90), Reid, Ambrose (Kishishev 79), Darren Bent.
Subs Not Used: Myhre, Diawara.
Goals: Reid 17.
Ref: P Dowd (Staffordshire).