The 32-year-old striker, who joined from Portsmouth in the summer, produced a cute finish to beat Thorsten Stuckmann two minutes before the break.
Preston's Paul Huntington saw a stoppage-time header superbly saved by 18-year-old George Long as United made it 13 games unbeaten in the league.
Preston should have taken the lead midway through the first half when Chris Beardsley found himself in space at the back post, but he could only direct his header over the visitors' crossbar.
However it was the Blades who were ahead at the interval after Kitson ran onto Tony McMahon's through ball to lift his shot over the onrushing Stuckmann.
Huntington then diverted a cross onto his own post before Long denied the defender at the right end with a fine save.