The Blades were tipped to challenge for the League One title this season, thanks to the appointment of Adkins as well as some eye-catching signings, but came unstuck as Gillingham struck in the first half through on-loan Spurs forward Emmanuel Osadebe and Adedeji Oshilaja. John Egan and Bradley Dack completed the scoring late on.
Fellow promotion contenders Wigan Athletic, relegated from the Championship last season, similarly struggled as they lost 2-0 at Coventry City.
Adam Armstrong, on loan from Newcastle United, bagged his first senior goal in the first half, and then doubled his career tally with his second after the break.
Doncaster took a late lead as the ball found its way into the back of the net when Harry Forrester was returning it to the Bury goalkeeper, but manager Paul Dickov instructed his side to allow Leon Clarke to equalise unopposed.
Results in full: Burton Albion 2-1 Scunthorpe United, Chesterfield 3-1 Barnsley, Colchester United 2-2 Blackpool, Coventry City 2-1 Wigan Athletic, Crewe Alexandra 0-0 Port Vale, Doncaster Rovers 1-1 Bury, Fleetwood Town 1-1 Southend United, Gillingham 4-0 Sheffield United, Rochdale 1-0 Peterborough United, Shrewsbury Town 1-2 Millwall, Swindon Town 4-1 Bradford City, Walsall 1-1 Oldham Athletic.