The Blades made it four wins on the bounce in Sky Bet League One with a thoroughly professional display against Swindon Town.
Second half goals from Neill Collins and Billy Sharp secured the win, whilst the clean sheet was very welcome at a ground where United conceded ten last season.
Reed took over from the suspended Baxter and Collins was fit to start as the Blades returned to the scene of the 5-5 play-off draw back in May. McEveley moved out to left back to accommodate Collins, who partnered Edgar in central defence.
United won an early corner but the serious chances in the opening ten minutes came from Swindon. Robert clipped over the crossbar after linking up with Kasim and Turnbull's run across the box saw Byrne fire straight at Howard.
United's first chance, on 15 minutes, was from the second phase of a corner but Basham could not get enough on the ball after Edgar headed down McEveley's cross. Home goalkeeper Vigouroux palmed over a 35-yard effort from Reed and from the resulting corner, on 24 minutes, Sammon hammered against the underside of the crossbar after the ball broke loose from Campbell-Ryce's delivery.
The action midway through the half was frantic as both sides looked for an opening. An acrobatic effort from Robert was off target and then Sammon deflected Sharp's cross over the top before Branco went close with a deft header from an inswinging free-kick.
Despite the game being open, the chances dried up as half-time approached, although a move between Sharp and Campbell-Ryce almost put the onrushing Reed in the clear.
Early in the second half Robert was prominent for the hosts, he was stopped by Reed's block and then a diving header was wide after he arrived late in the box. There was a nervous moment for Swindon on 57 minutes when goalkeeper Vigouroux looked to go around Sammon and his pass could have dropped anywhere but luck was with the custodian.
The action remained open, at both ends, Robert went close again with a shot on the turn on 63 minutes. A run from Campbell-Ryce put Swindon on the back foot and moments later a Woolford cross saw Sharp's diving header deflected wide.
The breakthrough finally arrived on 70 minutes and it was in front of the Blades fans. Reed delivered the corner, COLLINS rose highest and his header bounced over the goalkeeper, who appeared to be impeded by one of his defenders, before dropping into the corner of the net.
Swindon's fans were quiet and soon after they were stunned as United added a second. On a break, Woolford had the option of either of United's strikers and he went right to SHARP, who lost his marker and slotted past Vigouroux before heading off to celebrate with the Blades fans.
Vigouroux tried to get his own back as he clattered Sharp 30 yards from goal and was booked, whilst the Blades, in the remaining moments, were well organised in ensuring Swindon did not pressure Howard's goal.
United made a couple of late changes to run down the clock before the 1,117 Blades fans could celebrate on the trip home.
Swindon: Vigouroux, Robert, Williams, Turnbull, Traore, Kasim, Smith (Storey 67), Byrne, Stewart, Rodgers, Branco.
Unused: Brophy, Randall, Marshall, Belford, Barry, Landolo.
Blades: Howard, Freeman, Basham, Sharp, Collins, Sammon (Higdon 90), McEveley, Campbell-Ryce (Alcock 88), Reed, Adams (Woolford 61), Edgar.
Unused: McNulty, Long, McFadzean, McGahey.