Hull City 1 Sheffield United 3
Michael Tonge had a free volley inside the area early on, but Hull keeper Boaz Myhill pulled off a great save to keep the scores level.
The Tigers had a chance of their own midway through the half as clever play from Nick Barmby saw him produce an audacious lob inside the area, but Blades keeper Paddy Kenny did well as he tipped the ball over the bar.
Hull then went one better as the ball fell at the feet of Price on the edge of the area and he curled the ball emphatically into the top corner to send the hosts into a 1-0 lead.
The Blades fought back though and Ifill struck the leveller when his shot from the edge of the area found its way into the back of the net as it deflected off Andy Dawson and past the helpless Myhill.
Hull nearly went back into the lead before half-time but Kenny managed to turn a powerful strike from Leon Cort inside the area on to the post.
On the stroke of half-time United found themselves in front as great individual play from Webber saw him turn inside Cort and smash the ball into the bottom right-hand corner of the net from the edge of the area.
The Blades nearly stretched their lead early in the second half as from a David Unsworth corner, Armstrong saw his curling effort inside the box come back off Myhill's left-hand post.
On 52 minutes Armstrong did put United further in front after neat play inside the box involving Webber resulted in a low powerful shot rocketing past Myhill put the Blades 3-1 up.
It was nearly 4-1 to the visitors midway through the half as another curling corner from Unsworth was met by the head of Phil Jagielka, but he skimmed the crossbar from four yards.