Two goals inside a minute put Carlisle in the driving seat after an own goal had put their promotion rivals in front.
The Cumbrians went behind in the 20th minute when Hereford seized on a Paul Arnison mistake. David Brown raced down the right but his shot was superbly saved by Matty Glennon and rebounded to Adam Stansfield. The striker scuffed his shot but it cannoned off Lee Andrews and into the net.
On-loan Wigan youngster Magno Vieira got the equaliser when he met an exquisite Peter Murphy cross with a far-post header that flew in at the near post.
The Brazilian 19-year-old grabbed his second when Hereford lost possession from the restart, picking up the ball just inside the Bulls' half. He raced forward before unleashing a 25-yard thunderbolt that deflected off Andy Tretton and beat Ben Scott.
Two minutes into the second half Hereford's keeper was picking the ball out of his net for a third time.
Murphy got United's third with an 18-yard strike after Scott had flapped at a Brendan McGill cross.
A timely clearance by Tretton cutting out a Murphy cross stopped Karl Hawley adding a fourth in the 53rd minute.
Hereford didn't give up and they created chances of their own as they tried to get back on the scoresheet as Carlisle took their foot off the gas, but the Cumbrians coped with everything the visitors could throw at them.
Brown and Tamika Mkandawire fired wide and Stansfield had a 20-yard shot tipped one-handed round the post by Glennon before United replaced Vieira with Andy Preece in the 75th minute.
The veteran striker, returning from a lengthy injury, almost conjured a goal a minute later, turning Tretton, but his piledriver was just wide of the post.
Hereford knew they were beaten when their best player Jamie Pitman fired wide of the post with just four minutes left on the clock.
Carlisle boss Paul Simpson admitted his team weren't at their best, but said: "I'm not going to have a go at the players because we got the result.
"But we've ground out a win without the spark we've shown in recent weeks against a good side who will be up there at the end of the season." Hereford manager Graham Turner refused to speak to the press.