Annan weathered a second-half comeback from Clyde to record a narrow win in their Third Division encounter at Broadwood Stadium.
Scott Chaplain broke the deadlock in the 14th minute when he reacted quickest to Steven Swinglehurst's header to put the away side ahead.
Michael Daly then headed home Michael McGowan's left-wing cross just a minute later as the Black and Golds raced into a two-goal lead.
The visiting supporters were treated to a third goal, two minutes after the break, when Daly grabbed his second goal of the game with a close-range header.
The Bully Wee rallied and came back into the match on the hour mark thanks to John Sweeney's sweetly-struck volley.
Sweeney laid on the assist for Gary Graham 12 minutes from time as Jim Duffy's men sensed an unlikely comeback, but the Galabankies were able to hold out for their first away win of the season.
Clyde: Barclay, John Kane, Marsh, Oliver, Traynor (Neill 80), Fitzharris (McColm 46), Hay, Sweeney, Gilfillan (Graham 55), Watt, McCluskey. Subs Not Used: Rajovic, MacBeth.
Goals: Sweeney 60, Graham 78.
Annan Athletic: Mitchell, Blake, Monaghan, Swinglehurst (Peter Watson 84), McGowan, Love (Thorburn 64), McKechnie (John Watson 80), Chaplain, Sloan, Hopkirk, Daly. Subs Not Used: Summersgill, Donley.
Goals: Chaplain 14, Daly 15, 47.
Ref: John McKendrick