The result leaves the Blades still without a victory since their opening game of the season.
The home side went close to scoring inside the opening minute when Conor Coady's shot skimmed the top of the bar after he got on the end of a low cross from Lyle Taylor.
After Hartlepool's Jack Compton had a low shot saved by Mark Howard, Luke James dragged his shot well wide after finding himself free on the right-hand side of the area.
But Poole (37) scored with a fine finish, swiveling and firing past Howard after Darren Holden's long throw was headed on by Andy Monkhouse.
Scott Flinders protected Hartlepool's lead, saving from Michael Doyle's drive just before the break.
As the home side tried to draw level, Marlon King put a long-range attempt straight at Flinders while Jose Baxter's effort failed to test the keeper.
Substitute Ryan Hall also went close with a shot and Neill Collins' stoppage-time header was saved.