A late penalty from Chris Porter - his first goal of the season - ensured the Blades progressed to the second round of the FA Cup with Budweiser.
At the end of Colchester's ground which housed 410 Blades fans, the striker netted after 81 minutes after a 2-0 lead had been pegged back.
Harry Maguire netted his fifth goal of the season and an own goal extended the lead. However, second half goals from Macauley Bonne and Luke Garbutt gave the home side a lifeline before Porter's penalty.
The Blades team included four changes from the previous week's league encounter at Shrewsbury.
After a careful build-up, Miller was included from the start in the first team for the first time since Boxing Day 2013, whilst there were also recalls for Porter, Coady and McGinn. Flynn, Taylor and King dropped to the bench, whilst White was denied permission to play by his parent club, Leeds.
Lappin and Coady were handed the wide midfield roles, it was quickly apparent, but the game's first half chance fell to Bond, but his effort was deflected over by Collins, who recovered after mis-controlling. Incidentally, Collins had his head bandaged from the start to protect the head injury he sustained at Shrewsbury.
Then, for the next 12 minutes it was all Blades with no less than six efforts recorded in that time. It began with Miller laying off to McMahon, whose shot from an acute angle was bundled around a post by Walker.
The home goalkeeper, however, could do little to prevent the visitors taking the lead on 10 minutes. Following a foul on Porter, McGinn curled a free-kick to the back post where MAGUIRE's header looped over everyone before dropping in at the far post.
United's vocal travelling support had barely stopped celebrating when a second was added just two minutes later. This time Okuonghae gave the ball away, Porter progressed down the right and looked to pick out the well-positioned Miller or Doyle but the low cross was deflected by Eastman and trickled into the goal off the feet of goalkeeper WALKER.
Moments later, Miller's effort was blocked after a run down the left channel by Porter and Hill came close to his first Blades goal on 15 minutes when his 30-yard effort clipped the top of the crossbar. In addition, a 35-yard free-kick from McMahon was on target but saved by Walker.
Colchester managed to stem the momentum from the Blades but in terms of hitting back with goals, there was little to report in the first half. A Garbutt free-kick from the edge of the box was over and a speculative effort from Bonne was off target.
Collins needed treatment for his head injury late in the half and deep into injury-time, Colchester's best chance came from a move down the right but Eastmond's low volley was wide of Long's right post.
With their first effort on target, Colchester reduced the arrears soon after the restart. A deep cross from Garbutt skimmed off a head but BONNE continued his run at the back post and netted with a diving header.
The Blades hit back with chances falling to the front two but Miller shot over after cutting in from the right and Porter headed wide a cross from McMahon. On the hour Porter had a better chance to restore the two goal cushion when he lost his marker inside the six-yard area but he was unable to turn in another McMahon cross.
A Coady shot was straight at Walker before the Blades were punished for not converting the plenty of chances which were being created. On 64 minutes, there appeared little danger when a throw was half-cleared but GARBUTT's 30-yard effort was sweetly struck and nestled in the bottom corner of Long's goal.
Opportunities continued. Porter had a free header from McGinn's free-kick but Walker pushed the effort away, whilst Long kept out from Morrison at the other end. Clough made a couple of changes and the fast-paced action continued. Bean fired over for Colchester and Maguire, despite being under pressure, won another header from McMahon's cross.
Just as the game entered the final 10 minutes a crucial decision went United's way and with it came the lead. From Lappin's free-kick, Maguire's header was heading back across goal when it struck the hand of Okuonghae - referee Gibbs looked disinterested but was advised by one of his assistants that a penalty was the right decision. After deliberations, a spot-kick was awarded and PORTER waited patiently before sliding home, sending the goalkeeper the wrong way.
Late on Colchester threw defender Eastman forward and United introduced Taylor just before five minutes of added time was announced. Professionally, the Blades played clock down, completing the majority of the injury-time period in the Colchester half to book a place in Sunday's second round draw.
Colchester: Walker, Okuonghae, Eastmond (Vose 79), Morrison, Bond (Dickson 45), Bean, Eastman, Wilson, Gilbey, Garbutt, Bonne (Szmodics 87).
Unused: Cousins, Sanderson, Olufemi, Spence.
Blades: Long, Maguire, Hill, Doyle, Porter (Taylor 90), Miller (Baxter 75), McGinn (Flynn 68), Collins, Coady, Lappin, McMahon.
Unused: Howard, Cuvelier, King, Murphy.