Second-half goals from David Brown and Steve Guinan earned Hereford a home tie with Northampton Town in the second round of the LDV Vans Trophy.
The first half produced little in the way of constructive, attacking play with few chances on either side.
For Hereford the best opening came on 17 minutes when Guinan made good ground on the left and pulled the ball back for Danny Williams whose goalbound shot was blocked by Santos Gaia. Brown put the follow-up wide.
At the other end, Exeter's Barry McConnell powered in a drive four minutes later which Hereford's Matt Baker did well to parry.
On the stroke of half-time, an excellent move spanning the length of the pitch ended with Brown firing a shot against the post and wide.
If Hereford hoped this might lead to better things in the second period, they had less then 35 seconds to wait for their expectations to be realised.
Guinan did superbly to break away down the left and pulled the ball back for Brown who netted, seemingly off his shin, from six yards.
With Exeter striving to get back into the game, a fine tackle by Ryan Green foiled Sean Canham in a one-on-one situation on the edge of the penalty area and then Baker produced a brilliant diving save to foil Gareth Sheldon.
Shortly afterwards, Baker did well again to push away a shot from skipper Glenn Cronin and surpassed even that on 81 minutes when he dived a push a shot from substitute Les Afful over for a corner.
But despite Baker's involvement, Hereford always looked the more likely winners and the Bulls wrapped up their win three minutes from time when substitute Dean Craven slipped the ball to Guinan and the Bulls top scorer fired home his 12th goal of the season, with the help of a substantial deflection from Alex Jeannin.