A Jamie Murphy strike after 18 minutes saw the Blades become the first team to defeat promotion rivals Bournemouth at home since September the 29.
Scotland Under-21 international and former Motherwell star Murphy capitalised on a slip from full-back Marcos Painter to tap-in after his initial shot had rebounded back off a post.
The victory is United's fourth in a row and Wilson is hoping that his side can now stay clear of the chasing pack.
He said: "I am sure the league will change before the season is out but I hope it changes underneath us rather than involving us.
"I think we have fought very hard the last four games and been terrific. We have given ourselves a real chance.
"Anybody who puts a good run of wins together will have a great chance. At this moment we are keeping our side of the bargain."
Wilson's side limited the usually free-flowing Bournemouth team to half-chances and but for a Barry Robson shot hitting the bar and a late Ryan Flynn goal being disallowed, the scoreline could have been greater.
A delighted Wilson added: "I thought our performance was exceptional. We were physical and defended properly. What pleased me more than anything was how we thought our game plan out. There was some intelligent passing all the way through.
"I think they only had once chance all game, to come to here and have that type of performance was terrific. The players have really pleased me."