The Blades were unbeaten in the league at Bramall Lane and facing a team who had not won in their last 22 matches, but veteran striker Steve Howard headed Pools in front after seven minutes.
Michael Doyle equalised courtesy of a mistake by goalkeeper Scott Flinders before lifelong Sheffield Wednesday fan Ritchie Humphreys restored the visitors' lead early in the second half and Howard headed them a two-goal cushion after 72 minutes.
Harry Maguire's stoppage-time strike was too little, too late for the Blades, who began the day top of the table but slipped to second place after their surprise defeat.
"Overall, we can't really complain too much about the result because they took their chances better than we did and we defended poorly in key areas at key times in the game and that gave us a mountain to climb," said Wilson.
"We had a very dodgy offside decision against us and we had a penalty turned down when Harry Maguire was brought down right at the end. If we had got one of those then it might have been a different game but unfortunately we didn't."
Hartlepool boss John Hughes heaped praise on his players after seeing them win for the first time since he took charge last month.
He said: "I think the heavy pitch suited us because it slowed it down. Take nothing away from the guys though for their effort and commitment. To come away to the league leaders and score three goals is fantastic.
"Hopefully that will give us the confidence and the momentum to go and try and build on that. I'm delighted for the players. We knew they would have a right go at us in the second half so I said to the boys that they had to go and match it, and they won their one-on-one battles.
"Hopefully now we might see one or two of the players coming to training with a spring in their step and not feeling sorry for themselves. They've set a benchmark by beating the leaders away from home."
- Sports & Recreation
- Steve Howard
- Harry Maguire
- Scott Flinders
- Bramall Lane