Annan's task became more difficult when Peter Watson was dismissed for picking up a second booking on 76 minutes.
And Kyle MacAulay made sure of Elgin's win with a deflected shot past Greg Kelly with two minutes remaining.
Annan Athletic: Kelly, Jack Steele, McBeth (Steven Sloan 80), Watson, Neilson, Gilfillan, Muirhead, Jardine, Cox, Storey (Anson 82), Lewis Sloan (Bell 71). Subs Not Used: Summersgill, Jack.
Sent Off: Watson (76). Booked: Watson.
Elgin: Gibson, Niven, Trappers, Dempsie, MacDonald (Calder 61), Edwards, Gunn, MacAulay, Frizzel, Nicolson, David A Craig (Cameron 84). Subs Not Used: Steven Dunn, McLeod, Michael Dunn.
Booked: MacDonald, Gunn.
Goals: Niven 48, MacAulay 88.
Att: 416
Ref: W Collum
Source: BBC Sport
Source: BBC Sport