A harsh handball decision against the Shrimps' Fraser McLachlan gave Rob Purdie the chance to earn the Bulls a draw that sets up a potentially thrilling second leg at Edgar Street.
The Bulls, twice play-off losers, were also helped by another big decision when a Michael Twiss goal on 71 minutes was ruled out for offside with the television cameras showing it deserved to stand.
In many ways this was a game of two halves. After Hereford's Andy Williams volleyed wide in only the second minute Morecambe had the better of the early stages.
Twiss forced Wayne Brown into a neat save low to his right on nine minutes and Wayne Curtis also tested the Bulls keeper with a stinging shot.
However, Brown was unable to keep out the Shrimps' opener on 31 minutes. Twiss swung in a corner to the far post and central defender Jim Bentley steamed in at the far post to head home.
Moments later the Shrimps came close again with a Gary Thompson cross flashing inches wide of the goal before Hereford finally grabbed a foothold in the game towards the end of the first half.
Williams was denied a goal on the stroke of half-time by a wonderful save from Steven Drench and the Bulls maintained the pressure in the second period.
Craig Stanley was foiled by another neat Drench save before the controversial penalty decision when McLachlan was adjudged to have handled and Purdie struck the ball into the bottom right-hand corner despite the best efforts of Drench.
Hereford continued to press with Stanley firing inches wide and Williams headed over from an excellent Simon Travis cross.
After withstanding some intense pressure, Morecambe had the better chances at the end with Twiss denied a superb goal by a harsh offside flag and Thompson coming close again with another cross that fizzed just wide.
Brown was forced into two neat saves from Michael Howard and Garry Hunter as the Shrimps pushed forward but they couldn't add to their tally.