United, leading through Mark Duffy's first-half goal, looked on course for a superb victory in the capital before Patrick Bauer's stoppage-time goal rescued a point for the hosts.
Here, our man Danny Hall offers some talking points from the game.
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The Blades need to rediscover their cutting edge. Since scoring 14 goals in three games against Grimsby, Leyton Orient and Chesterfield, United have scored just three in their next three outings - two of which have come against teams reduced to nine men. They've struggled to convert their domination of all three games into goals, and one more here against Charlton would have killed the game and ensured a pretty comfortable win.
But they couldn't get one and although Dillon Phillips in the home goal was in inspired form at times, United boss Chris Wilder was disappointed afterwards that they didn't make their dominance count with goals and go two, three or even four goals ahead before the late sickener.
United are now 15 unbeaten in League One, a great record, but Wilder is not one for resting on any laurels and, as he revealed in his post-match Press conference, United's players have been told in no uncertain terms that they should have come away from this game with more than one point.
Would Matt Done have been an effective substitute? Easy to say, or ask, in hindsight but Done, dropped to the bench for the recalled Leon Clarke, offers far more than just a goal threat and is, put simply, a pain in the backside for defenders.
Clarke put a shift in and won his fair share of headers, but the amount of times Charlton's defenders took the easy option and passed back to Phillips was incredible and Done, with his electric pace and willingness to chase anything, would have forced them to go forwards instead at times.
Caolan Lavery, who did come on when Clarke was taken off, put in a similarly lung-busting shift and hopefully, a first goal in United colours - and a return to full, peak, match-fitness - will see him flying again.
Charlton fans really aren't keen on Roland Duchâtelet. Obvious one this, maybe, since they're intent on getting their owner out, but the game was halted after just a few seconds here when home fans threw balls, and a few flares for good measure, onto the pitch.
Officials at The Valley were obviously ready for it, as a team were on hand to clear the pitch, but it was an interesting - and saddening, really - insight into how the supporters, the lifeblood of any club, at any level, feel about their absent owner.
Alan Knill is a set-piece expert. Judging by his role in the celebrations that followed it, Knill played a big role in the set-piece which led to Mark Duffy's opener. Its simplicity was genius; nobody tracked Duffy's clever run and the United No.21 made no mistake from Daniel Lafferty's pass. Knill also devised a similarly impressive routine in United's draw at Scunthorpe, which saw Chris Basham put his side ahead.
United's fans certainly enjoyed their day in the capital, and showed off a couple of additions to their repertoire - including a version of Tag Team's Whoomp! paying homage to Paul Coutts and a future classic, adapting Wham's Last Christmas suggesting their heart is safe in the hands of Ethan Ebanks-Landell. The on-loan centre-half can't help but feel the love from the United fans, who gave their players a rousing reception at the end despite the late equaliser.