With Leeds United only drawing, and Middlesbrough losing, the Blades go into the international break as Championship leaders.
For Nigel Adkins's Hull, defeat sees them dumped to the bottom of the table.
The Blades named an unchanged team after their midweek win at Blackburn, meaning Paul Coutts remained on the bench.
For Hull, Jarrod Bowen and Kamil Grosicki dropped to the bench for the visitors.
Markus Henriksen had the first shot in anger, but it the Tigers captain's long-range effort was wide.
At the other end, Enda Stevens was unable to pounce after Burke failed to clear Basham's cross as the hosts tested out Hull's defence.
But the best chance fell to David McGoldrick - after clever approach play from Mark Duffy - but the United striker flicked his effort over the crossbar from close range.
The Tigers were forced into a first-half substitution when Fraizer Campbell limped off to be replaced by Nouha Dicko.
Reece Burke's goal-bound shot was deflected wide, but Stephen Kingsley's corner drifted over Dean Henderson's crossbar.
Hull - after being forced to defend in the early exchanges - came into the game as the half progressed, but they were nearly caught out when Duffy's back heel slipped in left wing-back Stevens, running down the right flank, but his shot was saved by David Marshall.
Dicko forced Henderson into a good save at the start of the second half, before the striker netted but the offside flag had already been waved.
While Billy Sharp hooked his effort wide, after Kieron Freeman's knockdown at the back post.
The Blades were indebted to Henderson on 67 minutes, the on-loan goalkeeper diving low to his left to keep out Henriksen's header.
And the hosts were in front moments later, McGoldrick sending Marshall the wrong way from the penalty spot after referee Peter Bankes spotted Tommy Elphick fouling Jack O'Connell.