United's hopes of a visit to Wembley in the Johnstone's Paint Trophy were ended on Tuesday night.
James Poole's first half goal gave Hartlepool United the area quarter-final berth on offer at Bramall Lane.
Chief Weir's team selection for the northern section second round fixture showed five changes with Howard, Westlake, Coady, Murphy and Taylor all included from the start. King and Taylor were strike partners as the formation appeared to be 4-4-2, although Doyle began in a deep position and Baxter in an advanced central role.
Less than a minute was on the referee's watch when the Blades recorded the fixture opportunity but from Taylor's cross Baxter's effort clipped the top of the crossbar. Hartlepool's first chance saw Compton shoot at Howard, whilst James missed a better effort, firing wide when in the clear after escaping the offside flag.
Murphy curled an effort wide but the Blades fell behind on 37 minutes. From Holden's long throw, Monkhouse flicked on and POOLE's acrobatic effort beat Howard for pace.
United's Taylor was booked for a foul and the remainder of the half saw the home side on top but the only chance to show for the efforts was a volley from Doyle, which was blocked by Flinders at the near post.
Early in the second half both sides exchanges chances - Baxter fired at Flinders after the referee had played an advantage and Holden shot wide for the visitors.
The Blades made a double change before the hour with Hall and Ironside replacing Murphy and Taylor but despite plenty of possession, efforts on the Hartlepool goal were sparse.
As the game entered the final 20 minutes, Baxter had two shots from the edge of the box blocked, whilst a blast from King was straight at Flinders and then Hall tried his luck with an effort, which was just over.
Late on Hall's curler was held by Flinders, whilst Ironside turned a Baxter corner wide. As four added minutes was announced, Baxter fired over and then, from a deep Doyle cross, auxiliary striker Collins headed at Flinders, which proved to be the final chance of the night.
Blades: Howard, Westlake, Maguire, Doyle, Taylor (Ironside 56), Baxter, Collins, Coady, King, Lappin, Murphy (Hall 56).
Unused: Hill, McGinn, Willis.
Hartlepool: Flinders, Austin, Walton, Poole, Monkhouse (Richards 83), Compton (Franks 79), Duckworth, Holden, James (Rodney 85), Burgess, Walker.
Unused: Rafferty, Sweeney.