Gary Hooper swept the fourth place Bulls into a 43rd minute lead at the Fraser Eagle Stadium and a bizarre Mark Roberts own goal seven minutes after the re-start ensured Graham Turner's side kept up the pressure on the League Two leaders.
The Accrington defender's terrible backpass evaded goalkeeper Kenny Arthur and, despite furious protests from Stanley boss John Coleman, the referee's assistant ruled the ball across the line.
If there was some controversy surrounding Hereford's second, then there could be little doubt at the result.
High-flying Hereford started brightly and Simon Johnson twice went close to putting the visitors in front inside the opening five minutes. The winger saw his first effort blocked by Darren Kempson, before firing wide moments later.
Clint Easton then curled a 25-yard free-kick just past the upright before Sherjill MacDonald forced a smart save from keeper Arthur.
Accrington gradually clawed their way back into the game and David Mannix and Leam Richardson both tested Wayne Brown in the Bulls goal.
But Hereford continued to carve out the better chances and the impressive MacDonald on-loan from West Brom, saw his shot cleared off the line.
Hooper gave the Bulls a deserved lead two minutes before half-time when he latched on to Johnson's cross.
Hereford then wrapped up the points seven minutes after the re-start courtesy of Roberts' mistake.
The visitors continued to press forward in search of a third and Toumani Diagouraga's long-range effort was kept out by Arthur.
Stanley piled on the pressure late on as they searched for a way back into the game, but Hereford held on comfortably to secure a convincing victory.