Bukayo Saka, called up to the England squad by Gareth Southgate this week, nodded Arsenal in front on the hour mark as Sheffield United's difficult start to the campaign continued. Substitute Nicolas Pepe then added a second to put the game safe as Arsenal bounced back from their 3-1 defeat at Liverpool in the league. David McGoldrick's fine curling strike on 83 minutes made it a nervy finale but Arsenal held on.
Mikel Arteta's men, who beat Liverpool on penalties in the Carabao Cup in midweek, played their third match in seven days and they looked sluggish at times against a United side that were winless and goalless in their first three Premier League matches of the season ahead of Sunday's match at the Emirates.
In a low-key first half, Arsenal defender David Luiz escaped a possible red card in the opening minutes when he appeared to pull Oliver Burke's shirt when he was through on goal but the VAR ruled in the centre-back's favour.
It took until the 28th minute for the game's first attempt on goal but Eddie Nketiah's header was tame and no problem for Aaron Ramsdale in the Sheffield United goal. Ramsdale was at full stretch to deny Pierre-Emerick Aubameyang moments later after the Arsenal forward curled an effort goalwards. Aubameyang then went down in agony following a stern challenge from Sander Berge and after treatment on the field, he was cleared to continue.
The second half followed a similar pattern to the first, with Aubameyang going close once more but he could not divert Dani Ceballos' pass into the net. Sheffield United continued to toil in attack, with Chris Wilder unable to call on club record signing Rhian Brewster, who was not registered in time to feature following his move from Liverpool.
Arteta brought Pepe on to add more variety to the Arsenal attack and it wasn't long before the home side were ahead. Hector Bellerin's cross from the right was met perfectly by Saka, who nodded the ball home for his first goal at the Emirates.
Pepe then added a second three minutes later, side-footing a clinical strike past Ramsdale to double Arsenal's lead and give Arteta's men some breathing space. McGoldrick's superb strike reduced the deficit late on but the visitors could not find an equaliser.
Wilder's men, meanwhile, are on a run of seven consecutive defeats in the Premier League and they remain in the bottom three amid a testing start to the 2020-21 season.