The Foxes were handed a ninth minute lead by Steven Howard but had to wait until the 71st minute before doubling their advantage through Andy King.
Then there were anxious moments late on as Karl Broadhurst pulled a goal back for the Bulls, but City hung on for their eighth straight win.
Hereford were first to threaten when Matt Done tested David Martin from 22 yards before King hit back for Leicester with a 25-yard shot which soared over the bar.
City then had a penalty appeal turned down after Kris Taylor blocked a Matt Oakley drive with his arm. But Leicester weren't to be denied when after nine minutes Matt Fryatt crossed for Howard to thump the ball beyond Craig Samson from 12 yards.
The Hereford keeper then dived smartly to his left to divert a Fryatt close-range shot, before Martin did well to hold on to a volley from Lionel Ainsworth.
Howard had another clear sight of goal thanks to an accurate cross from Fryatt, but he was disappointed to direct his header straight at the keeper.
And just before the break, Howard returned the compliment to set up Fryatt, who was foiled by a strong challenge by the keeper.
Paul Dickov replaced the injured Fryatt at half-time then Howard had two chances soon after the restart with a miscued shot before driving an Oakley cross wide.
City went close on the hour mark when King's 25-yard free-kick extracted a fingertip save from Samson, who a short while later was grateful when Howard hoisted a 20-yard drive over the bar.
Hereford conjured up a rare chance on 64 minutes when Steve Guinan found himself in the clear, but Martin was quickly off his line to block the striker's shot.
At the other end Howard set up King whose wayward shot failed to hit the target, but City finally doubled their lead on 71 minutes when Oakley set up King, who scored with a crisp drive from 16 yards.
Hereford gave themselves a lifeline on 79 minutes when Broadhurst took full advantage of a hesitant home defence to head in a deep free-kick from Lionel Ainsworth.
Then there was an anxious moment for Leicester in the final minute of normal time when Hereford were awarded a free-kick 25 yards in front of the goal but there was relief all around when Taylor's effort flew just wide to allow Leicester to record their eighth successive home win.