Annan moved to within two points of 10-man Elgin in the Third Division after coming from behind to win 2-1.
Two first-half goals from Jordan McKechnie gave Annan all three points to boost their play-off hopes.
Paul Millar headed Elgin ahead after six minutes, beating Annan goalkeeper Alex Mitchell.
Annan drew level 20 minutes later thanks to McKechnie, who scored his fourth goal of the season with a low effort from just outside the area.
McKechnie then put Annan ahead before half-time after sweeping home David Cox's cross from the left.
The home side had to play the second half with 10 men after Stuart Leslie saw red for a second bookable offence on the brink of half-time but Annan held off their opponents in the second half to seal the win over the side who sit just above them in the league.