The visitors pulled one back through Steven Canning but Albion's hope was short-lived as Bryan Gilfillan's shot put Annan 3-1 up on 70 minutes.
And Chris Jardine slotted home a fourth for the South of Scotland side.
Annan Athletic: Jamieson, Muirhead, Neilson, Aitken, Steele (Jardine 65), Gilfillan (Lewis Sloan 90), Steven Sloan, MacBeth, Cox, Harty (Amaya 74), Halsman. Subs Not Used: Summersgill, Felvus.
Goals: Halsman 42, 56, Gilfillan 70, Jardine 80.
Albion: Gaston, Reid, Benton, Donnelly, McGowan (Meechan 49), Gemmell, Canning, Stevenson, Lawless, McLeod (Smith 59), Love, Meechan (Ferry 64). Subs Not Used: Nugent, Gilmartin.
Goals: Canning 67.
Att: 517
Ref: S Nicholls
Source: BBC Sport
Source: BBC Sport