A goal from skipper Jim Bentley earned the Shrimps a fourth away win of the campaign at Edgar Street.
Bentley scored with a header on 24 minutes after a superb far post cross from on loan Simon Hackney.
Phil Jevons should have made it 2-0 five minutes later when a Mark Duffy shot came back off the post and fell perfectly for the Morecambe top scorer but he somehow missed the target from close range.
Hereford bounced back with Barry Roche making good saves from Marc Pugh and Leon Constantine. The Bulls put pressure on the Morecambe goal in the second period but Morecambe defended superbly and held on to claim a confidence-boosting win.
Shrimps' boss Sammy McIlroy stuck with the same side that drew 1-1 with Grimsby on Saturday for the game.
Hereford: Barrett; Green, Jones Rose, Valentine, Pugh, McQuilken, Lunt, McCallum (Manset 43), Sonko (Done 46), Constantine. Subs not used: Adamson, Preston, Gwynne, Downing, King.
Morecambe: Roche; Parrish, Bentley, Haining, Wilson; Duffy (Curtis 89), Drummond, Panther, Hackney (Wainwright 89), Jevons (Stanley 66), Mullin. Subs not used: Davies, Moss, Artell, Hunter.
Ref: Mr P Gibbs.
Att: 1,208 (36 from Morecambe)