For Sheffield United, Chris Wilder’s return has not quite gone to plan. Last season, the club were able to mount a successful promotion campaign while reaching the FA Cup semi-finals but being a Premier League struggler has placed a great strain. “We haven’t won enough,” he said, more than happy for the competition to provide a fillip.

“We did a job on them, didn’t we?” he continued, aware of his newfound status as a social media meme. “We never really allowed the crowd to get on top of us.”

Related: FA Cup roundup: Maidstone United pull off another shock to reach round four

If Gillingham were occasionally dangerous, there was little chance for a giantkilling. Instead, Priestfield reminded of the high tide that clubs like Sheffield United, despite a squad of talented players, must swim against in the top echelon. William Osula, a 20-year-old Dane, scored twice to advertise he has something to offer in the battles ahead. Late on, James McAtee, a clear man of the match, scored two more to further smooth progress.

Wilder had rotated his squad but not significantly. A manager who made his bones in the Football League’s lower reaches did not fancy being downed by former peers. Ben Brereton Díaz, Friday’s loan signing from Villarreal, coming off the bench pointed to further promise. The Stoke-bred Chile international arrived on 72 minutes, his side’s passage all but secured.

Stephen Clemence had also respected the competition’s traditions in choosing the same team that beat Colchester on New Year’s Day, League Two playoff contention sidelined in the hope of puncturing Premier League pride. When Conor Masterson, their centre-back, set on an early mazy dribble, the home fans rose, only for the danger to be closed down. Such a cycle of excitement and disappointment was regularly repeated.

The hosts’ defence was marshalled by Max Ehmer, his deportment rather reminiscent of one-time Gillingham favourite Steve Bruce. The aim was not to get caught on the counter but in the 14th minutes, after the overlapping full-back Cheye Alexander was dispossessed, a long diagonal from McAtee found Osula, whose shot beat Jake Turner from the tightest angle. The visiting fans at the uncovered away end took time to realise their team had scored.

“You see the blistering pace of a Premier League side,” said Clemence, proud of his players but critical, too. “We probably can do better with their goals. We wouldn’t like to concede them in a League Two game.”

The usual path to an FA Cup shock is the underdog holding on and then taking their chances but Gillingham failed to follow that blueprint. As an offside Oli Hawkins had a header saved, Wilder’s abrasive exhortations filled the Medway air.

His return to Bramall Lane has seen the manager unsparing in his criticism, in public and doubtless behind closed doors. His team responded accordingly to his blasts almost instantly. Andre Brooks’s shot was parried into the path of Osula and converted with precision. A hat-trick might have followed but Osula volleyed over the rebound from Cameron Archer’s shot.

“This is where you get really judged as a player,” said Wilder, highlighting the potential damage of losing to a League Two team. “What’s your attitude like?”

The visitors were put through a modicum of defensive paces after the break, Connor Mahoney’s dead-ball expertise causing problems; Hawkins might have done better with a corner within his orbit. When Mahoney smashed a shot wide, an unsighted section of the home support went up in celebration.

Similar followed as Ehmer rose to head another Mahoney special off the inside of the post but back out. “If that goes in the place would have erupted,” said Clemence.

Within moments, McAtee had scored his first, converting Oliver Norwood’s pass, the goal his performance had deserved. His second soon followed, celebrated with a somersault.

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Agony, disappointment, back to League Two reality for Gillingham. The Priestfield resident DJ marked the final whistle with a burst of Morrissey’s Suedehead. Sheffield United and their manager, meanwhile, entered their two-week hiatus with relief that Gillingham had not done a job on them.