Hereford United 0 Exeter City 2
Tony James' poor back-pass let in James Mackie for the opener after 61 minutes and Jon Challinor's fine strike shortly afterwards effectively settled the issue.
Hereford had much the better of the first period with only Les Afful and Andy Taylor testing Craig Mawson with Exeter goal attempts.
Hereford, on the other end, carved out a number of opportunities with Andy Williams foiled by Chris Todd's block in the first minute with Guy Ipoua's header well turned around a post by goalkeeper Paul Jones a minute later.
James and Jon Brady also fired in efforts before Craig Stanley came closest for the Bulls, driving in a shot from 25 yards which beat Jones and thudded against the bar before rebounding into the keeper's arms.
Rob Purdie drove wide following a fine Jamie Pitman pass and then, seconds before the interval steered a shot straight at Jones after a good run and cross by Ipoua.
After the break, Exeter came out with renewed determination and James' weak back pass was missed by Mawson to let in Mackie who scored from a narrow angle.
Then Challinor controlled the ball neatly before lifting a shot into the corner of the net.
Hereford pushed forward in an attempt to pull something out of the game but failed to find a way through.
The best effort came from Ipoua who headed a Simon Travis cross narrowly over the bar nine minutes from time.
"We had six silly minutes in the game and they proved costly," said Bulls boss Graham Turner. "We played very well in the first half and missed some good opportunities."