The teams' differing priorities were revealed by the fact that Leicester made eight changes from the side which played at Sunderland on Saturday, while Hereford were unchanged from their previous game against Bury.
Despite their considerable reshuffle it was the visitors who had much the better of the first period.
On nine minutes, only a brilliant save by Hereford's Wayne Brown kept out an Iain Hume shot at the expense of a corner.
And Hume was unlucky again when his header came back off the bar when the half-cleared flag-kick was returned to the centre.
Hume was involved in the opening goal on 27 minutes, heading a pass to Elvis Hammond who controlled the ball before turning to lash an unstoppable shot past Brown.
Hereford's best chance came, ironically, courtesy of the Foxes.
A Tim Sills header was going across the goal until Richard Stearman's boot deflected the ball goalwards, forcing goalkeeper Conrad Logan to bring off a flying save.
Hereford came out revitalised after the break and levelled through a Rob Purdie spot-kick after Logan felled Stuart Fleetwood. Logan, despite denying a goalscoring opportunity, was only yellow carded.
Logan produced flying saves from Fleetwood and Sills as Hereford pressed forward, but it was the visitors who grabbed the vital third goal in the 66th minute when Josh Low's corner was flicked on for Stearman to score at the far post.
Leicester extended their lead ten minutes later in controversial circumstances.
Levi Porter raced into the area and, with the ball running out of play, was brought down by Trent McClenahan. Referee Russell Beeby awarded a penalty but, showing incredible inconsistency, sent off the Australian before Hume scored from the spot.
In the closing stages, Beeby levelled up the red card count by dismissing Patrick Kisnorbo for pushing Sills.