Duffy, who later limped-off through injury, applied the finishing touches to an ingenious set-piece routine after Leon Clarke had been hauled down.
United enjoyed several opportunities to stretch their lead but Dillon Phillips came to Charlton Athletic’s’ rescue on several occasions. His contribution proved crucial when, deep into added time, Bauer turned home from close-range.
Charlton, with new manager Karl Robinson watching from the stands, are one of Wilder’s picks to challenge for promotion this season. Despite making a slow start to the campaign, they entered this match in fine form and immediately posed a threat.
But one of United’s greatest strengths of late has been their ability to take charge of games in a variety of different manners. Here, after keeping the dangerous Josh Magennis and Nicky Ajose at arms length, it was a free-kick which ended them in front.
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Wilder’s assistant Alan Knill, who takes great pride in devising innovative routines, looked a happy man when Duffy converted after being sent through by Paul Coutts. Duffy, who excelled throughout, deserved his goal and would have grabbed another after the interval but for Phillip’s fine save. But it was also fitting that Coutts and Fleck were involved in the deception which handed United the lead. They impressed too.
The contest, though, remained alive until the end with Bauer pouncing to set up a grandstand finish.
Predictably, given the home support’s grievance with owner Roland Duchâtelet, a protest quickly brought a halt to the game. With tiny plastic taxis being thrown onto the pitch and a flare being lit in one of the stands, play resumed after a brief hiatus.
Charlton, given their experience of coping with such incidents, coped better with the interruption. Magennis beat Ethan Ebanks-Landell to a second minute header which sent Ajose scampering through. United’s defence managed to shepherd him away to safety but, moments later, was powerless to prevent Johnnie Jackson fizzing a dangerous centre across Simon Moore’s six yard box. Any sort of touch from Magennis, who had flung himiself at the ball, would surely have resulted in a goal.
United began to pose some questions of their own around the quarter-of-an-hour mark. Daniel Lafferty put Charlton on the back foot with a dangerous run but Jack O’Connell’s shot was blocked.
Wilder had insisted beforehand that he was not afraid to change a winning team. As a result, despite starting the wins over Shrewsbury Town and Bury, Matt Done found himself beginning this match on the bench with Clarke taking his place alongside Billy Sharp in attack. Lafferty also featured after recovering from illness while Duffy returned following injury.
Duffy tried to weave his way through the Charlton rearguard when Billy Sharp and Clarke combined in the 16th minute but, like Ajose earlier, was eventually crowded out.
In the 31st minute, though, United took the lead. Clarke was awarded a free-kick just outside the penalty area and although Coutts, Lafferty, John Fleck and Duffy all appeared ready to shoot, the ball was instead dispatched down the flank. Duffy, who had peeled away, seized possession and with Charlton’s rearguard still trying to fathom what was going on, threaded the ball past Phillips and into the net.
Sharp tested Phillips handling early in the second-half with an overhead kick which was well-placed but lacked power. Fleck did put plenty of weight behind his angled drive soon after but the ball was scrambled clear.
Then, on the hour, Phillips produced a wonderful parry to deny Duffy when he finally shot following two clever feints.
Charlton had even more reason to thank their goalkeeper, who foiled Jack O’Connell during the closing stages, when Bauer scrambled home following a free-kick conceded by Lafferty.
Charlton Athletic: Phillips, Foley, Jackson (Chicksen 52), Bauer, Lookman, Crofts (Botaka 81), Magennis, Ajose (Novak 61), Pearce, Ulvestad, Fox. Not used: Beeney, Konsa, Lennon, Hanlan.
Sheffield United: Moore, Fleck, O’Connell, Basham, Sharp, Wright (Freeman 46), Coutts, Ebanks-Landell, Duffy (Scougall 76), Lafferty, Clarke (Lavery 66). Not used: Ramsdale, Hussey, Done, Chapman.
Referee: Graham Scott (Oxfordshire).