John Sweeney's first-half penalty at Annan was enough for Clyde to move off the bottom of the Scottish Third Division table.
The hosts had a great opportunity to go ahead in the 44th minute when Scott Chaplain tried his luck from 30 yards out, but his superb effort was tipped over by goalkeeper Jamie Barclay.
The Bully Wee took the lead less than a minute later when Sweeney scored his seventh goal of the season from the spot following Iain Chisholm's foul on Stefan McCluskey.
The visitors defended resolutely in the second half, barely giving Annan an opportunity to get into their penalty box and held on to record a welcome victory.
Annan Athletic: Mitchell, Chisholm (Black 88), McNiff, Swinglehurst, McGowan, Orsi,Jardine (Sloan 72),Chaplain, Love, Hopkirk, Murray (Hawke 57). Subs Not Used: Shepherd, Monaghan.
Clyde: Barclay, Scullion, Gray, Fordyce, McDonald, Nicoll, Hay, Sweeney, McColm (Fitzpatrick 88), Watt (McGachie 76), McCluskey (Fitzharris 78). Subs Not Used: Rajovic, Lyden.
Booked: Nicoll. Goal: Sweeney 45 pen.
Ref: Craig Charleston