Chris Wilder's resurgent side have now scored in the first 15 minutes in four of those five Championship matches and climbed to third in the early-season table despite a two-point deduction.
With the box loaded, Hull worked a corner short down their left and played it back to last man Belloumi but O'Hare easily stole possession and within seconds the ball was in their net through Hamer's third goal of the season.
Abdus Omur's well-struck free-kick forced Blades goalkeeper Michael Cooper into a smart stop before the break.
However, it was the visitors who looked more likely to get the second goal, more than once passing up decent opportunities on the counter, with Hull guilty of over-playing in dangerous areas.
Vini Souza's close-range shot was well kept out by Ivor Pandur in the City goal after the break but there was nothing the Croatian could do to stop the Blades doubling their lead.
Once again it came from a Tigers corner. The ball was initially cleared up as far as substitute Rhian Brewster near the halfway line on the right and his diagonal ball was kept in by Kieffer Moore, who easily shoulder-barged Liam Millar off it.
The Welshman linked up with Brooks who cutely set up McCallum for his first goal for the club.
German midfielder Mehlem should have got the home side on the scoreboard from Lewie Coyle's cross but could not get his header on target and they remain on just two goals for the season.
The Tigers travel to Stoke next Friday, while the Blades host Derby a week on Saturday.