Annan scored in either half to record a 2-0 victory over Albion and climb into second place in League Two.
Annan goalkeeper Kenny Arthur tipped Mark McGuigan's header onto the bar and Albion survived a goalmouth scramble in a lively opening.
The visitors were not so lucky on 35 minutes as Josh Todd headed home Scott Davidson's cross for his sixth goal of the season.
Todd turned provider eight minutes into the second half when he released Kenneth Mackay, who smashed a right-footed drive into the bottom corner from 15 yards.
McGuigan summed up Albion's afternoon as he headed straight at Arthur when it appeared easier to score, leaving his side to reflect on their first defeat in seven games.