Craig Fagan also went close for Hull with a fierce 25-yard drive, while Northern Ireland striker Stuart Elliott had a goal disallowed for offside.
Wednesday had their chances but strikers David Graham and Lee Peacock missed wastefully when it appeared easier to score.
Sheffield Wednesday assistant manager Kevin Summerfield:
"I can't remember Nicky Weaver having a shot to save before they scored, but
you have to concentrate for 90 minutes.
"We are not playing badly but we are not scoring goals and we are not getting into scoring positions.
"We lack that killer instinct and we won't win games until we score goals."
Hull: Myhill, Lynch (Price 59), Cort, Collins, Dawson, France, Welsh, Delaney, Barmby (Green 78), Paynter (Elliott 63), Fagan.
Subs Not Used: Duke, Andrews.
Goals: Price 87.
Sheff Wed: Weaver, Simek, Coughlan, Wood, Gilbert, O'Brien, Whelan (Brunt 45), Adams, Murphy, Peacock (Eagles 69), Graham (Agbonlahor 74).
Subs Not Used: Lee, Hills.
Booked: Gilbert.
Att: 21,329
Ref: M Atkinson (W Yorkshire).