A goal deep into injury-time earned United a place in the second round of the Capital One Cup.
Substitute Neill Collins was the hero, netting with a powered header very late on to defeat Morecambe in front of 785 travelling fans.
United, semi-finalists in the competition last year, recorded a first competitive win for Nigel Adkins.
New loanee Edgar was named in the starting XI just a day after making his season-long switch to the Blades. The Canadian international partnered captain McEveley in the heart of the defence as boss Adkins made a total of seven changes from Saturday's defeat at Gillingham.
United's first competitive fixture at the Globe Arena saw the first chance fall to McNulty, on five minutes, but he could not connect after James Wallace and Freeman linked up. In the early exchanges, Beeley cut in and shot at Howard for the home side, whilst Freeman stopped both Molyneux and Wildig with tackles in the box in the same move.
After the initial battles, the Blades began to create a number of opportunities. Basham headed over a Scougall corner, whilst McNulty was heavily involved, he fired shots either side of the goal and was also part of the build-up for chances for Sammon, who was also off target, and Freeman, who was very close with a volley after a one-two with the Scottish striker.
As half-time approached, Morecambe hit back with a couple of chances of their own. Devitt's shot appeared to move in the air but Howard adjusted and parried away and then a shot from Edwards was blocked in a crowded penalty area.
For the start of the second period Adams was introduced on the left for Woolford and the substitute took a minute to cause problems for the home side but his shot, after Scougall's pass, was blocked by the goalkeeper's legs.
It set the tone for United to get on top and further chances followed in the next ten minutes. From McNulty's held up cross, Sammon's header was on target but deflected wide by a defender, then Edgar headed wide a Scougall cross, before Kieran Wallace curled over after Adams laid off.
As the hour mark approached Sammon was wide with a shot from the edge of the box after Scougall robbed Fleming, whilst the home side's first chance of the half came when Parrish headed over a corner from the right.
Former Blade Miller was introduced for Morecambe but Mullin was the next to go close, finding the sidenetting, whilst the Blades were back on the attack in the last ten minutes. Edgar's header was kept out from a corner, Roche again kicked away from Adams and a McNulty effort was deflected wide.
With extra-time looming, Devitt broke away for the home side but made the wrong decision when approaching the box, he attempted to cross but was crowded out by Freeman and the penultimate chance saw Adams clip a free-kick over the crossbar.
There was time for just one more chance and it provided the winning goal, deep into injury-time. James Wallace delivered the left-wing corner and substitute COLLINS rose to head powerfully past Roche.
There was little time for Morecambe to stage a response as the Blades booked the second round place on offer.
Morecambe: Roche, Beeley, Edwards, Devitt, Molyneux (Miller 80), Mullin, Goodall, Wildig (Kenyon 57), Fleming (Ellison 71), Wilson, Parrish.
Unused: McGowan, Thompson, Ryan, Doyle.
United: Howard, Freeman, J Wallace (Reed 90), Basham, McNulty, Scougall, Woolford (Adams 45), Sammon, McEveley, K Wallace, Edgar (Collins 84).
Unused: Sharp, Collins, Higdon, Long, McFadzean.