Colin Cooper’s side made it two wins on the bounce with another convincing display to pick up another deserved victory thanks to a first half stunner from James Poole.
There was an early scare for Pools when a Lyle Taylor cross from the left found Conor Coady in space at the far post and his shot on goal just clipped the crossbar on its way over.
As they did at Mansfield on Saturday though, Pools reacted well to the early threat and went on to enjoy a really strong spell of possession.
With the hosts looking a little fragile at the back, Cooper’s men looked to take full advantage with a direct approach and constant chasing.
Jack Compton had the first shot on target for his side with a low effort from just inside the box but Blades keeper Mark Howard was equal to it.
James Poole then picked out Luke James with a neat ball to set his strike partner running in on goal. Luke shoed a great first touch to take it past his man and push on into the box but his final shot on goal saw the ball drag wide of the far post.
Pools refused to let Sheffield United settle on the ball, pushing and chasing for everything and with the mid-way point of the half passed, it was the visitors who were on top.
With no goals coming so far, the Blades began to edge their way forward and began to cause Pools a few more problems.
Andy Monkhouse put in a good double block in the box to deny the cross from the right before Simon Walton did the same on the edge of the box.
But just as the home fans may have begun to expect their team to take the advantage into the break, Pools upped the ante by breaking the deadlock.
James Poole met an Andy Monkhouse ball to send a sweet left-footed volley past Howard from 12 yards to make it 1-0 to his side on 37 minutes.
The lively forward – clearly playing with plenty of confidence - tried a more ambitious effort with his right just minutes later but saw that effort go over the bar.
Sheffield United had a good chance on the stroke of half time to draw level; Christian Burgess rose highest to send a corner out of the danger area but his clearance found Michael Doyle on the edge of the box and he returned on the volley. Scott Flinders though, largely untested for the first half, reacted quickly to get down and hold the effort and the lead for his team going into half time.
Cooper’s men came out after the break looking bright again and they had a great chance to double the lead within minutes of the re-start.
Brad Walker, who played another big part on his return to the side, picked out Darren Holden down the left with a great ball and the left back did just as well to break forward and send a teasing ball across the box. His cross evaded the blue and white shirts in the box but did earn Pools another corner.
Jose Baxter had the first shot of the second half for his side on 54 minutes but his strike from the edge of the box was a comfortable one for Flinders to hold.
At the other end, more good work from Poole inside the area saw him pick out Jack Compton on the right of the area but his final shot curled wide of the far post as the home supporters began to voice their frustration.
The home side upped their urgency as the half wore on and began to see more of the ball in the final third and there were a couple of crucial clearances from Burgess, while Flinders was also called into action to keep the hosts at bay.
The Blades were getting plenty of crosses into the box but, with 15 minutes remaining, they were proving routine for Flinders as a hard working Pools protected their lead.
Neil Austin got in a great block to deny Marlon King from meeting a Conor Coady pass inside the box as Pools were doing more and more defending with the final whistle in sight.
Sub Ryan Hall, who gave the hosts more spark going forward, sent a shot fizzing past the post inside the final ten minutes, while Flinders collected a curling effort from the same player just minutes later.
Former Pools loanee Neill Collins went up front for the hosts in the dying minutes and he met a freekick to send bullet header which found only the arms of Flinders.
It was a tense finale to the game, with four added minutes drawing things out further, but Pools held on for what was a thoroughly deserved victory to ensure it is their name in the draw for the Area Quarter Finals of the Johnstone’s Paint Trophy.
Full Time: Sheffield United 0 Pools 1
Booked: Poole (66)
Att: 4189 (249 Pools)
Pools: Flinders, Duckworth, Austin, Burgess, Holden, Compton (Franks 79), Walton, Walker, Monkhouse (Richards 83), Poole, James (Rodney 85)
Subs Not Used: Rafferty, Sweeney
Sheffield United: Howard, Westlake, Maguire, Doyle, Taylor (Ironside 56), Baxter, Collins, Coady, King, Lappin, Murphy (Hall 56)
Subs Not Used: Hill, McGinn, Willis